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 Sethophormididae Haeckel, 1881
Subfamily †Neosciadiocapsinae Pessagno, 1969
Genus †Coniforma Pessagno, 1969