Liroceras is the type genus of the clydonautiliacean

Clydonautilaceae

The Clydonautilaceae is a superfamily within the nautiloid order Nautilida characterized by smooth, generally globular, shells with nearly straight sutures, in early forms but developing highly differentiated sutures in some later forms...

 family, Liroceratidae

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...

, 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 has a range from the Mississippian to the Permian, longest of the Liroceratidae. It has been found the North America, Europe, China and the East Indies. Condraoceras

Condraoceras

Condraoceras is a liroceratid 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...

differs in having a circular cross section and shallow ventral and lateral lobes. Bistrialites

Bistrialites

Bistrialites is an involute, globose Clydonautilacean belonging to the Liroceratidae with a reniform whorl section, large funnel shaped umbilcus, smooth surface except for spiral ornament in the region of the umbilical shoulder. Bistrialites comes from the Lower Carboniferous of...

also has a reniform whorl section but differs in ahving a large funnel-shaped umbilicus.

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.