[SOLVED] Subgroups of Order Three The problem statement, all variables and given/known data 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?