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 Triospyridinae Haeckel, 1881
             01 Genus Acrospyris Haeckel, 1881
             02 Genus Aegospyris Haeckel, 1881
             03 Genus Anthospyris Haeckel, 1881
             04 Genus Brachiospyris Haeckel, 1881
             05 Genus Ceratospyris Ehrenberg, 1847
             06 Genus Cladospyris Ehrenberg, 1847
             07 Genus Corythospyris Haeckel, 1881
             08 Genus Dendrospyris Haeckel, 1881
             09 Genus Dictyocircus Jørgensen, 1905
             10 Genus Giraffospyris Haeckel, 1881
             11 Genus Gorgospyris Haeckel, 1881
             12 Genus †Hexaspyridium Haeckel, 1887
             13 Genus Liriospyris Haeckel, 1881
             14 Genus Lophospyris Haeckel, 1881
             15 Genus Pentaspyris Haeckel, 1881
             16 Genus †Petalospyrella Haeckel, 1887
             17 Genus Petalospyris Ehrenberg, 1847
             18 Genus Semantidium Haeckel, 1887
             19 Genus Semantiscus Haeckel, 1887
             19.0 [Genus Sematiscus Agarkov, 2005, nom. null.] see Genus Semantiscus Haeckel, 1887
             20 Genus Semantrum Haeckel, 1887
             21 Genus Taurospyris Haeckel, 1881
             22 Genus Therospyris Haeckel, 1881
             23 Genus Triceraspyris Haeckel, 1881
             24 Genus Triospyrium Haeckel, 1887