Division Bacillariophyta Engl. & Gilg (1919) see Phylum Bacillariophyta Engl. & Gilg (1919)
   Class Coscinodiscophyceae Round & R.M. Crawford (1990) - radial centrics
     Subclass Thalassiosirophycidae Round & R.M. Crawford (1990) see Class Mediophyceae Medlin & Kaczmarska (2004)
       Order Thalassiosirales Glezer & I.V. Makarova (1986)
         1 Family Thalassiosiraceae M. Lebour (1930), nom. cons.
         2 Family Skeletonemataceae M. Lebour (1930)
         3 Family Stephanodiscaceae Glezer & Makarova (1986)
         4 Family Lauderiaceae (Schütt) Lemmerm. (1899)