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 Coccodiscidae Haeckel, 1862
           Subfamily Coccodiscinae Haeckel, 1862
             01 Genus Astrophacus Haeckel, 1881
             02 Genus Coccocyclia Haeckel, 1881
             03 Genus Coccodiscus Haeckel, 1862
             04 Genus Heliosestrum Haeckel, 1881
             05 Genus †Heliostylus Haeckel, 1881
             06 Genus Lithocyclia Ehrenberg, 1847
             07 Genus Periphaena Ehrenberg, 1873
             08 Genus Phacodiscus Haeckel, 1881
             09 Genus Phacostaurus Haeckel, 1881
             10 Genus Phacostylus Haeckel, 1881
             11 Genus Trigonactum Afanasieva & Amon, 2005, nom. null. see Genus Trigonactura Haeckel, 1881
             12 Genus Sethostylus Haeckel, 1881