Phylum Radiolaria Müller, 1858 see Subphylum Radiozoa Cavalier-Smith, 1987
   Superclass Polycystina Ehrenberg, 1838 see Superclass Polycystinia Ehrenberg, 1838
     Class Nassellaria Ehrenberg, 1847
       Order Spyridinata Ehrenberg, 1847
         Family Triospyrididae Haeckel, 1881
           Subfamily †Dipodospyridinae Haeckel, 1881
             1 Genus †Dipodospyris Haeckel, 1881
             2 Genus Dorcadospyris Haeckel, 1881
             3 Genus Gamospyris Haeckel, 1881
             4 Genus Stephanospyris Haeckel, 1881, nom. illeg.