Condraoceras is a liroceratid

Liroceratidae

Liroceratidae is an extinct family of nautilids, shelled marine molluscs, belonging to the Clydonautilaceae, consisting of generally smooth, involute, nautiliconic forms with a small umbilicus...

 from the Pennsylvanian of North America and Lower Permian of Europe with a compressed, involute, nautiliconic shell; subcircular whorl section; small umbilicus with a rounded shoulder; suture with shallow ventral and lateral lobes; and narrow subcentral siphuncle.

Liroceras

Liroceras

Liroceras is the type genus of the clydonautiliacean family, Liroceratidae, and is characterized by a rapidly expanding, subglobular, nautiliconic shell with a reniform whorl section, small umbilicus, essentially straight sutures, and a siphuncle with a variable but not marginal position.Liroceras...

, from the same time and type of the family, differs in having a reniform whorl section and essentially straight sutures at maturity. Peripetoceras

Peripetoceras

Peripetoceras is a genus in the Clydonautilacean family, Liroceratidae. It can be recognized by its smooth, involute shell with a deep small umbilicus with rounded shoulders and steep convex wall; whorl section with flattened venter, rounded ventral shoulders and convergent slightly convex flanks;...

, another related genus, has a flattened venter, slight ventral and lateral lobes in the suture, and a siphuncle offset dorsally from the center.

References

• Bernhard Kummel, 1964. Nautiloidea -Nautilida; Treatise on Invertebrate Paleontology
  Treatise on Invertebrate Paleontology
  The Treatise on Invertebrate Paleontology published by the Geological Society of America and the University of Kansas Press, is a definitive multi-authored work of some 50 volumes, written by more than 300 paleontologists, and covering every phylum, class, order, family, and genus of fossil and...
  
  , Part K. Geol Soc of America and Univ of Kansas press, R.C. Moore (ed) -- Liroceratidae K444 -K447.