Subphylum [Vertebrata] Cuvier, 1812 - vertebrates see Infraphylum Vertebrata Lamarck, 1801
   Class Agnatha Cope, 1889
     Subclass †Thelodonti Kiaer, 1932
       Order †Furcacaudiformes Wilson & Caldwell, 1998 - fork-tailed thelodonts
         Family †Furcacaudidae Wilson & Caldwell, 1998
           Genus †Canonia Vieth, 1980
             1 †Canonia grossiᵀ Vieth, 1980
             2 †Canonia costulata Märss, Wilson & Thorsteinsson, 2002