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My initial reaction was to write direct products between an abelian and non abelian groups — for example, $Z_5\times D_2$. However, I realized they are both abelian so I am a little stuck. I can't think of any subgroup that is not abelian. Could it be a semidirect product or something? If so, could you give me a hint? My knowledge of semidirect products is sketchy to say the least.