†Placodermi McCoy, 1848
   †Arthrodira Woodward, 1891
     †Brachythoraci Gross, 1932
       †Eubrachythoraci Miles, 1971
         †Pachyosteomorphi Stensiö, 1944 - pachyosteomorphs
           †Aspinothoracidi Stensiö, 1959
             Genus †Heintzichthys Whitley, 1933
               1 †Heintzichthys gouldii (Newberry, 1885)