Phylum Radiolaria Müller, 1858 see Subphylum Radiozoa Cavalier-Smith, 1987
   Superclass Polycystina Ehrenberg, 1838 see Superclass Polycystinia Ehrenberg, 1838
     Class Nassellaria Ehrenberg, 1847
       Order Cyrtidinata Haeckel, 1862
         Superfamily Acropyramidoidea Haeckel, 1881
           Family Acropyramididae Haeckel, 1881
             01 Genus Acropyramis Haeckel, 1881
             02 Genus Bathropyramis Haeckel, 1881
             03 Genus †Cephalopyramis Haeckel, 1881
             04 Genus Cinclopyramis Haeckel, 1879
             05 Genus Cladachnidium Afanasieva & Amon, 2005, nom. null. see Genus Cladarachnium Haeckel, 1881
             06 Genus Enneapleuris Haeckel, 1887
             07 Genus Haliphormatidium Afanasieva & Amon, 2005, nom. null. see Genus Haliphormartidium Campbell, 1951
             08 Genus Litharachnidium Haeckel, 1887
             09 Genus Litharachnium Haeckel, 1860
             10 Genus Peripyramis Haeckel, 1881
             11 Genus Plectopyramis Haeckel, 1881
             12 Genus Polypleuris Haeckel, 1887
             13 Genus Sethopyramis Haeckel, 1881
             14 Genus Spongopyramis Haeckel, 1887