Is there a subgroup $\displaystyle H$ of $\displaystyle A_4$ such that the quotient group $\displaystyle {A_4}/H \cong S_3$? I know I could just go through the possibilities, but is there a very quick reason why the answer should be "no"?
Is there a subgroup $\displaystyle H$ of $\displaystyle A_4$ such that the quotient group $\displaystyle {A_4}/H \cong S_3$? I know I could just go through the possibilities, but is there a very quick reason why the answer should be "no"?