A group G has exactly 8 elements or order 3

[nowimpsbball]

A group G has exactly 8 elements of order 3 (Unanswered as of 1/31)

How many subgroups of order 3 does G have?

So we have 8 elements, its prime decomposition is 8=2^3. The number of different ways to get factors is how many subgroups, at least that is what I interpret from my notes...so there are 2^3, 2*2^2, and 2*2*2, so three different ways to get factors, am I doing this right?

Thanks

 

[d_leet]

Do you mean G has 8 elements OR order 3, or do you mean G has 8 elements OF order 3.

 

[nowimpsbball]

Do you mean G has 8 elements OR order 3, or do you mean G has 8 elements OF order 3.

g has 8 elements OF order 3, my bad

 

[mathwonk]

every subgroup of order three has how many elements of order three?

and how many common elements of order three do two distinct subgroups of order three have?