Class Actinopoda Calkins, 1902 see Parvkingdom Actinopoda Calkins, 1902
   Subclass Radiolaria Müller, 1858 see Phylum Actinopoda Calkins, 1902
     Superorder Polycystina Ehrenberg, 1838 see Class Polycystinea Ehrenberg, 1838
       Order Nassellaria Ehrenberg, 1875 see Class Nassellaria Ehrenberg, 1847
         Superfamily Acanthodesmiacea Haeckel, 1862 see Order Spyridinata Ehrenberg, 1847
           Family Triospyrididae Haeckel, 1881
             01 Genus Anthospyris Haeckel, 1881
             02 Genus Androspyris Haeckel, 1887
             03 Genus Archiphaena Haeckel, 1887 see Genus Archiphatna Haeckel, 1881
             04 Genus Brachiospyris Haeckel, 1881
             05 Genus Ceratospyris Ehrenberg, 1847
             06 Genus Clathrobursa Haeckel, 1881
             07 Genus Corythospyris Haeckel, 1881
             08 Genus Dendrospyris Haeckel, 1881
             09 Genus Desmospyris Haeckel, 1881
             10 Genus Dorcadospyris Haeckel, 1881
             11 Genus Gorgospyris Haeckel, 1881
             12 Genus Hexaspyris Haeckel, 1887
             13 Genus Lamprospyris Haeckel, 1881
             14 Genus Liriospyris Haeckel, 1881
             15 Genus Lophospyris Haeckel, 1881
             16 Genus Patagospyris Haeckel, 1881
             17 Genus Petalospyris Ehrenberg, 1847
             18 Genus Petalospyrella Haeckel, 1887
             19 Genus Psychospyris Riedel & Sanfilippo, 1971
             20 Genus Rhodospyris Haeckel, 1881
             21 Genus Semantrum Haeckel, 1887
             22 Genus Tholospyridium Haeckel, 1887
             23 Genus Tholospyris Haeckel, 1881
             24 Genus Triospyrium Haeckel, 1887