Phylum Porifera Grant, 1836 - sponges
   Class Hexactinellida Schmidt, 1870 - hexactinellids
     Subclass Amphidiscophora Schulze, 1886
       Order Amphidiscosa Schrammen, 1924 see Order Amphidiscosida Schrammen, 1924
         Family †Stiodermatidae Finks, 1960
           01 Genus †Calcihexactinia Sdzuy, 1969
           02 Genus †Protohyalostella Chapman, 1940 see Genus Protohyalostelia Chapman, 1940
           03 Genus †Rigbyella Mostler & Mosleh-Yazdi, 1976, nom. illeg.
           04 Genus †Thoracospongia Mehl, 1996
           05 Genus †Hyalostelia Zittel, 1879
           06 Genus †Astroconia Sollas, 1881
           07 Genus †Divaricospongia Rigby & Maher, 1995
           08 Genus †Acanthactinella Hinde, 1887
           09 Genus †Itararella Kling & Reif, 1969
           10 Genus †Rhakistella Weller, 1931
           11 Genus †Stioderma Finks, 1960
           12 Genus †Uralonema Librovich, 1929
           13 Genus †Irpaspongia Mehl & Mostler, 1994