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"?

- Jan 15th 2010, 06:40 AMBoysilverIs there a subgroup H of A4 such that A4 / H isomorphic to S3?
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"?

- Jan 15th 2010, 08:14 AMtonio
- Jan 15th 2010, 08:22 AMBoysilver
Great, thanks.