Phylum Radiolaria Müller, 1858 see Subphylum Radiozoa Cavalier-Smith, 1987
   Superclass Polycystina Ehrenberg, 1838 see Superclass Polycystinia Ehrenberg, 1838
     Class Stauraxonaria Afanasieva & Amon, 2005
       Order †Pyramidata Afanasieva & Amon, 2005
         1 Family †Tormentidaeᵀ Nazarov & Ormiston, 1983
         2 Family †Ruzhencevispongidae Kozur, 1980
         3 Family †Pyramispongiidae Kozur & Mostler, 1978
         4 Family †Cavaspongiidae Pessagno, 1973