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**HallsofIvy** (Of course, if a group is Abelian, them "left" and "right" are the same- all cosets. All groups of order 5 or less are Abelian so you must go up to order to 6 to have a chance at an example. But, if I remember correctly, since 6= 2(3), the product of two primes, a group of order 6 also has all subgroups normal. Of course 7 is itself prime and therefore Abelian (all groups of prime order are cyclic groups so you really, I think, need to go to order 8 to find a group in which the left cosets are different from the right cosets.)