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There are five groups of order 8: three of them are Abelian and the other two are not.

These are

1. C8, the group generated by a where a8 = 1

2. C4xC2, the group generated by a and b where a4 = b2 = 1

3. C2xC2xC2, the group generated by a, b and c where a2 = b2 = c2= 1

4. the dihedral group

5. the quaternion group

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Q: What is the numbers of groups of order 8 upto isomorphisms?
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