Two groups are isomorphic if the correspondence between them is one-to-one and the "multiplication"
table is preserved. For example, the point groups 
and 
are isomorphic groups, written
or 
(Shanks 1993).
Isomorphic Groups
See also
Jordan-Hölder TheoremExplore with Wolfram|Alpha
References
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, 1993.Referenced on Wolfram|Alpha
Isomorphic GroupsCite this as:
Weisstein, Eric W. "Isomorphic Groups." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IsomorphicGroups.html