Phylum Dinoflagellata Engl. (1903)
see Superclass Dinoflagellata Bütschli, 1885
Subphylum Dinokaryota Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (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) [monotypic]
1 Family Ptychodiscaceae Lemmerm. (1899)
2 Family Amphitholaceae Kof. & J.R. Michener ex Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
see Family Amphilothaceae Kof. ex Poche (1913)
3 Family Brachydiniaceae Sournia (1972)
see Family Brachidiniaceae Sournia (1972)