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
           1 Subfamily †Dipodospyridinae Haeckel, 1881
           2 Subfamily Archiphatninae Haeckel, 1881
           3 Subfamily Triospyridinae Haeckel, 1881
           4 Subfamily Tholospyridinae Haeckel, 1887
           5 Subfamily †Androspyridinae Haeckel, 1887
           6 Subfamily †Nephrospyridinae Haeckel, 1887