Division Bacillariophyta Engl. & Gilg (1919) see Phylum Bacillariophyta Engl. & Gilg (1919)
   Class Bacillariophyceae Haeckel (1878) - pennates
     Subclass Bacillariophycidae D.G.Mann (1990) - raphid diatoms
       Order Achnanthales P.C.Silva (1962)
         1 Family Achnanthaceae Kütz. (1844)
         2 Family Cocconeidaceae Kütz. (1844)
         3 Family Achnanthidiaceae D.G.Mann (1990)