Domain Eucaryota
   Subdomain Chlorota Doweld (2001)
     Kingdom Chlorobiota C.Jeffrey ex Doweld (2001) - plants see Subkingdom Viridiplantae Caval.-Sm. (1981)
       Subkingdom Lycopodiobiotina Doweld (2001)
         Phylum Isoëtophyta Doweld (2001)
           Subphylum Isoëtophytina Doweld (2001)
             Class Isoëtopsida Rolle (1884)
               1 Order †Takhtajanodoxales Snigirevskaya (1980) see Order Isoëtales Prantl (1874)
               2 Order Isoëtales Prantl (1874) [monotypic]