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 Peridiniphycidae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
         Order Gonyaulacales F.J.R. Taylor (1980)
           Suborder Gonyaulacineae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
             Family Gonyaulacaceae Er. Lindem. (1928)
               [Genus †Hexasphaera R.F.A. Clarke & Verdier (1967), incertae sedis]