After Engeser, 1998, Young, Vecchione & Mangold, 1996-2000 [“The Tree of Life”], and Shevyrev, 2006, with some order-information from the “Wikipedia”

A list of some †“Orthoceratida” taxons.

<==o Cephalopoda Cuvier, 1797 (cephalopods; pääjalkaiset, mustekalat)
   |?-o †Nectocarididae Conway Morris, 1976 sensu Smith & Caron, 2010 [disputed (kröger et al, 2011), morphology suggest larval or juveline radiodont (PanArthropoda) (pers. opinion)]
   |  |?- †Vetustovermis planus Glaessner, 1979 [Vetustodermis (lapsus calami)]
   |  |?- †Petalilium latum Lupo & Hu, 1999 [Petalium (lapsus calami)]
   |  `-- †Nectocaris pteryx Conway Morris, 1976
   `--+--o †Plectronocerida Flower, 1964 [nom. transl. Zhuravleva, 1972 ex subordo Plectronoceratina Flower, 1964] [paraphyletic Ellesmeroceratoidea Flower, 1950]
      |  |--o †Balkoceratidae Flower, 1964
      |  |  |-- †Balkoceras gracile Flower 1964
      |  |  `--o †Theskaloceras Chen & Teichert, 1983
      |  |     |-- †T. subrectum Chen & Teichert, 1983
      |  |     `-- †T. benxiense Chen & Teichert, 1983
      |  `--o †Plectronoceratidae Kobayashi, 1935
      |     |-- †Eodiaphragmoceras sinense Chen & Qi, in Chen, Chen, & Qi, 1979
      |     |-- †Jiagouceras Chen, 1979
      |     |-- †Lunanoceras longatum Chen & Teichert, 1983
      |     |?- †Multicameroceras Kobayashi, 1933
      |     |--o †Palaeoceras Flower, 1954
      |     |  |-- †P. mutabile Flower, 1954
      |     |  `-- †P. undulatum Flower, 1954
      |     |-- †Paraplectronoceras pyriforme Chen & Qi, 1979
      |     `--o †Plectronoceras Ulrich & Foerste, 1933; L.Cam. NEAs.
      |        |-- †P. cambria (Walcott, 1905)
      |        |-- †P. exile Flower, 1964
      |        |-- †P. gracile Flower, 1964
      |        `-- †P. liaotungense Kobayashi, 1935
      `--+?-o †Protactinocerida Chen & Qi, 1979 [paraphyletic Ellesmeroceratoidea Flower, 1950]
         |  `--o †Proactinoceratidae Chen & Qi, in Chen et al. 1979
         |     |--o †Physalactinoceras
         |     |  |-- †P. speciosum Chen & Teichert, 1983
         |     |  |-- †P. papilla Chen & Teichert, 1983
         |     |  |-- †P. globosum Chen & Qi, in Chen et al. 1979
         |     |  |-- †P. cf. globosum Chen & Qi, in Chen et al. 1979
         |     |  `-- †P. qiushugouense Chen & Teichert, 1983
         |     |-- †Proactinoceras
         |     |--o †Sinoeremoceras Kobayashi, 1933
         |     |  `-- †S. taiziheense Chen & Teichert, 1983
         |     `-- †Wanwanoveras exigum Kobayashi, 1933
         |?-o †Yanhecerida Chen & Qi, 1979 [paraphyletic Ellesmeroceratoidea Flower, 1950]
         |  `--o †Yanheceratidae Chen & Qi, 1979
         |     |-- † Aetheloxoceras Chen & Qi, 1979
         |     |-- †Archendoceras Chen & Qi, 1979
         |     |-- †Oonendoceras Chen, 1981
         |     `-- †Yanheceras Chen & Qi, 1979
         |?- †Ellesmerocerida Flower, in Flower & Kummel, 1950 [Endocerotida: Ellesmerocerotina] [paraphyletic Ellesmeroceratoidea Flower, 1950]
         `--o Palcephalopoda [Nautiloidea sensu lato] [incl. paraphyletic †Orthoceratida Kuhn, 1940]
            |?-o †Endoceratoidea Teichert, 1933 [nom. transl. Teichert, 1964 ex ordo Endoceroidea Teichert, 1933]
            |  |--o †Endocerida Teichert, 1933 [nom. correct. Teichert, 1964 pro Endoceroidea Teichert, 1933] [Allotrioceratiformes Starobogatov, 1983]]
            |  |  `==o †Proterocamerocerina Flower, 1958
            |  |     `==o †Proterocameroceratidae
            |  |        |-- †Manchurocheratidae
            |  |        |==o †Chihlioceratidae
            |  |        |  `-- †Allotrioceratidae
            |  |        |-- †Emmonsoceratidae
            |  |        |-- †Najaceratidae
            |  |        `--o †Endocerina
            |  |           `==o †Piloceratidae
            |  |              `-- †Endoceratidae
            |  `-- †Inteljocerida Balashov, 1960 [nom. correct. Teichert, 1964 pro Inteljoceratida Balashov, 1960]
            |?-o †Actinoceratoidea Teichert, 1933 [nom. transl. Teichert, 1964 ex ordo Actinoceroidea Teichert, 1933]
            |  `-- †Actinocerida Teichert, 1933 [nom. transl. Teichert, 1964 pro Actinoceroidea Teichert, 1933] sensu Kröger & Mapes, 2007 [Actinoceroida; Actinoceratoidea]
            |?- Nautiloidea Agassiz, 1848 sensu stricto [nom. transl. Diener, 1913 ex subordo Nautiloidea Agassiz, 1848] [Nautiloda; Nautilomorphi; Tetrabranchiata] (Nautilius-like cephalopods; helmiveneidenkaltaiset mustekalat)
            |?-o †Orthoceratoidea Kuhn, 1940 [nom. transl. Teichert, 1967 ex subordo Orthoceracea Kuhn, 1940]
            |  |==o †“Clinoceratidae” [paraphyletic Orthocerida]
            |  |  |-- †Clinoceras
            |  |  |-- †Centroonoceras
            |  |  |-- †Whitfieldoceras
            |  |  |?- †Whiteavesites
            |  |  `-- †Ascocerida Kuhn, 1949 [nom. correct. Teichert, 1964 pro Ascoceracea Kuhn, 1949]
            |  |--o †Dissidocerida Zhuravleva, 1964 [nom. correct. Shevyrev, 2006 pro Dissidoceratida Zhuravleva, 1964]
            |  |  |-- †Troedssonellidae
            |  |  `-- †Polymeridae
            |  |-- †Bajkalocerida Zhuravleva, 1972 [nom. correct. Shevyrev, 2006 pro Dissidoceratida Zhuravleva, 1972]
            |  `--+?- †Slemmestadoceras attavus (Brøgger, 1882) Kröger, 2008 [Orthoceras attavus Brøgger, 1882]
            |     |?- †Kyminoceras
            |     `-- †Orthocerida [nom. transl. et correct. Teichert, 1964 ex subordo Orthoceracea Kuhn, 1940] [Pseudorthoceratida Flower & Caster, 1935 sensu Engeser, 1998; Pseudorthoceratoidea; Pseudorthocerataceae Flower & Caster, 1935 (nom. transl. Sweet, 1964 ex Pseudorthoceratidae Flower & Caster, 1935); Pseudorthoceratida Baskow, 1960 sensu Shevyrev, 2006] [incl.? Michelinoceratida Flower, 1950 sensu Shevyrev, 2006]
            `--o Neocephalopoda Lehmann & Hillmer, 1980 [Angusteradulata Lehmann, 1967](uusmustekalat)
               |-- †Arionoceras [Arionoceratidae Dzik, 1984] [paraphyletic Orthocerida]
               |--o †Lamellorthoceratidae [paraphyletic Orthocerida]
               |  |-- †Lamellorthoceras
               |  |-- †Arthrophyllum
               |  `-- †Gorgonoceras
               `==o †Bactritida: Bactritina
                  |-- †Bactrites
                  |--+--o †Bactritida: Agoniatitina
                  |  |  |?- †Anetoceras
                  |  |  |-- †Mimoceratoidea [Mimocerataceae]
                  |  |  `--+-- †Agoniatitoidea [Agoniatitaceae]
                  |  |     `-- †Auguritoidea [Auguritaceae]
                  |  `-- †Ammonoidea Zittel, 1884 (ammoniitit, ammonites)
                  `--+--o †Michelinocerida [Michelinoceratida Flower, 1950; Michelinoceroida Engeser, 1998]
                     |  `--o †Michelinoceratidae [Orthoceratidae in partim] [paraphyletic Orthocerida]
                     |     `--o †Michelinoceras Foerste, 1932
                     |        |-- †M. primum Flower, 1962
                     |        |-- †M. chaoi Chang, 1957 [?Orthoceras (Kröger, Beresi & Landing, 2007)]
                     |        |-- †M. beianense Ying, 1989 [?Orthoceras (Kröger, Beresi & Landing, 2007)]
                     |        |-- †M. paraelongatum Chang, 1962 [?Orthoceras (Kröger, Beresi & Landing, 2007)]
                     |        `-- †M. sinoceraforme Lai, 1960 [?Orthoceras (Kröger, Beresi & Landing, 2007)]
                     `-- Coleoidea Bather, 1888 [Dibranchiata] (nykymustekalat)

Reference(s):