A group G has exactly 8 elements or order 3

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nowimpsbball
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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
 
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Do you mean G has 8 elements OR order 3, or do you mean G has 8 elements OF order 3.
 
d_leet said:
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
 
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?