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 Spongodiscata Haeckel, 1862
         Family Spongodiscidae Haeckel, 1862
           01 Genus Amphirhopalum Haeckel, 1881
           02 Genus Chitonastrum Haeckel, 1881
           03 Genus Dictyocoryne Ehrenberg, 1860
           04 Genus Euchitonia Ehrenberg, 1860
           05 Genus Ommatodiscus Stöhr, 1880
           06 Genus Perichlamydium Ehrenberg, 1847
           07 Genus Porodiscus Haeckel, 1881
           08 Genus Rhopalastrum Ehrenberg, 1847
           09 Genus Spongaster Ehrenberg, 1860
           10 Genus Spongodiscus Ehrenberg, 1854
           11 Genus Spongotrochus Haeckel, 1860
           12 Genus Stylochlamydium Haeckel, 1881
           13 Genus Stylodictya Ehrenberg, 1847
           14 Genus †Stylospongia Haeckel, 1862
           15 Genus Tessarastrum Haeckel, 1887
           16 Genus †Tholodiscus Kozlova, 1972
           17 Genus Trigonastrum Haeckel, 1887