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)
       Subclass Gymnodiniphycidae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
         Order Ptychodiscales Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
           Family Ptychodiscaceae Lemmerm. (1899)
             Subfamily Ptychodiscoideae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
               1 Genus Balechina Loebl. & A.R. Loebl. (1968)
               2 Genus Berghiella Kof. & J.R. Michener (1911)
               3 Genus Ceratoperidinium Margalef ex A.R. Loebl. (1980)
               4 Genus Kolkwitziella Er. Lindem. (1919) see Genus Diplopsalis Bergh (1882)
               5 Genus Lissaiella Lindemann (1928) see Genus Amphidinium Clap. & J. Lachm. (1859)
               6 Genus Lophodinium Lemmerm. (1910)
               7 Genus Ptychodiscus F. Stein (1883)
               8 Genus Sclerodinium J.D. Dodge (1981)