Division Bacillariophyta Engl. & Gilg (1919) see Phylum Bacillariophyta Engl. & Gilg (1919)
   Subdivision Bacillariophytina Medlin & Kaczmarska (2004) see Subphylum Bacillariophytina Medlin & Kaczmarska (2004)
     Class Bacillariophyceae Haeckel (1878) - pennates
       01 Order Fragilariales P.C.Silva (1962)
       02 Order Tabellariales Round (1990)
       03 Order Licmophorales Round (1990)
       04 Order Raphoneidales see Order Rhaphoneidales Round (1990)
       05 Order Thalassionematales Round (1990)
       06 Order Rhabdonematales Round & R.M. Crawford (1990)
       07 Order Eunotiales P.C.Silva (1962)
       08 Order Lyrellales D.G.Mann (1990)
       09 Order Mastogloiales D.G.Mann (1990)
       10 Order Dictyoneidales D.G.Mann (1990)
       11 Order Cymbellales D.G.Mann (1990)
       12 Order Achnanthales P.C.Silva (1962)
       13 Order Naviculales Bessey (1907)
       14 Order Thalassiophysales D.G.Mann (1990)
       15 Order Bacillariales Hendey (1937)
       16 Order Rhopalodiales D.G.Mann (1990)
       17 Order Surirellales D.G.Mann (1990)