Division Haptophyta Hibberd
   Class Prymnesiophyceae D.J. Hibberd (1976) see Class Coccolithophyceae Rothm. (1951)
     Subclass Prymnesiophycidae (D.J. Hibberd) Cavalier-Sm. (1986) see Class Prymnesiophyceae D.J. Hibberd (1976)
       "Heterococcoliths"
         "Muroliths"
           1 Order †Eiffellithales Rood, Hay & Barnard (1971)
           2 Order Zygodiscales Young & Bown (1997)
           3 Order Stephanolithiales (Bown & Young, 1997)
           4 Order Syracosphaerales Ostenfeld (1899)
           5 Order Rhabdosphaerales Ostenfeld (1899)