A question about normal subgroups and index Let $G$ be a group, and $H$ be a normal subgroup of $G$. $|H|=11$ and $[G:H]=24$. Let there be $x \in G$ and $x^{11}=e$. Show $x \in H$. 
Would like hints etc' on how to solve this. Is proving that $x \in H$ basically means showing that $Hx=H$? 

Hint:
Look at the coset of $\;xH\;$ of $\;x\;$in the quotient group, and use (or prove, if you haven't yet seen this):
$$ord(xH)\mid ord(x)\;,\;\;\text{and also}\;\;ord(xH)\mid ord\left(G/H\right)=[G:H]$$
