Division Dinoflagellata Engl. (1903) see Superclass Dinoflagellata Bütschli, 1885
   Subdivision Dinokaryota Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) see Superclass Dinokaryota Fensome et al., 1993
     Class Dinophyceae Pascher (1914)
       Order Thoracosphaerales Tangen (1982), incertae sedis [monotypic] see Order Peridiniales Haeckel (1894)
         Family Thoracosphaeraceae J. Schiller (1930)
           1 Genus †Schizosphaerella Deflandre & P.J.L. Dang. (1938)
           2 Genus Thoracosphaera Kamptner (1927)