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