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There was a hint for this question saying to first prove that at least one of the subgroups has index 2 in G. So far I am not sure how to even start this problem. I know that the orders of [tex] H_1, H_2, H_3 [/tex] must divide the order of G, but this doesn't give much information. I was thinking of trying to show that the order of G must have a factor of 2, since [tex] |G| = [G: H_i]|H_i| [/tex] but with only the information given, I have no idea how to go about it.

Could someone offer a hint or two on how to proceed? thanks.