After Parker, 1982, and de Laubenfels, 1955

<==o Lithistida
   |?- †Astroboliidae
   |?- †Chonellidae
   |?- †Cnemidiastridae
   |?- †Plinthodermatiidae
   |?- †Scytaliidae
   |?- Jereopsiidae [not recognized by Parker, 1982]
   |?- Kaliapsidae [not recognized by Parker, 1982]
   |?- Leiodorellidae [not recognized by Parker, 1982]
   |?-o Tetracladina [not recognized by Parker, 1982]
   |  |-- †Aulocopiidae
   |  |-- †Archaeoscyphiidae
   |  |-- †Chenendoporidae
   |  |-- †Hallirhoidae
   |  |-- †Plinthosellidae
   |  |-- †Astrocladiidae
   |  |-- †Aulaxiniidae
   |  |-- †Jereidae
   |  |-- Discodermiidae
   |  `-- †Phymaraphiniidae
   |--o †Eutaxicladina [not recognized by Parker, 1982]
   |  |-- †Astylospongiidae
   |  |-- Gignouxiidae
   |  |-- †Chiastoclonellidae
   |  `-- †Pseudoverruculinidae
   |--o †Anomocladina
   |  |-- †Cylindrophymatidae
   |  |-- †Eospongiidae
   |  `-- †Mastosiidae
   |--o Triaenosina [Desmophorina; ?Megamorina]
   |  |?- †Dorydermatidae
   |  |?- †Halobrachiidae
   |  |?- †Isoraphiniidaw
   |  |-- Theonellidae
   |  |-- Corallistidae
   |  `-- Pleromidae
   |--o Rhabdosina
   |  |-- Scleritodermidae
   |  |-- Neopeltidae
   |  `-- Siphonidiidae
   `--o Anoplina
      |-- Leiodermatiidae
      |-- Desmanthidae
      `-- Vetulinidae

Reference(s):