Phylum Radiolaria Müller, 1858 see Subphylum Radiozoa Cavalier-Smith, 1987
   Superclass Polycystina Ehrenberg, 1838 see Superclass Polycystinia Ehrenberg, 1838
     Class Stauraxonaria Afanasieva & Amon, 2005
       Order †Pyramidata Afanasieva & Amon, 2005
         Family †Pyramispongiidae Kozur & Mostler, 1978
           1 Genus †Discokatorella Kozur & Mostler, 1994
           2 Genus †Intermediella Lahm, 1984
           3 Genus †Katorella Kozur & Mostler, 1981
           4 Genus †Kulacella Kozur & Mostler, 1981
           5 Genus †Neopaurinella Kozur & Mostler, 1981, nom. illeg.
           6 Genus †Paurinella Kozur & Mostler, 1981
           7 Genus †Pyramispongia Pessagno, 1973
           8 Genus †Rikivatella Kozur & Mostler, 1981
           9 Genus †Triassospongosphaera Kozur & Mostler, 1981