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**[SOLVED] Subgroups of Order Three**

**Homework Statement**

Let G be a subgroup containing exactly eight elements of order three. How many subgroups of order three does G have?

**The attempt at a solution**

This problem was discussed in class today. The professor said that G has four subgroups of order three. I didn't follow his explanation very well so I didn't understand why. Since there are eight elements of order three, wouldn't each of these elements constitute a subgroup of order three so G has at least eight subgroups of order three?