I was making some exercises on group theory when I came across this problem:
Suppose G is a finite group and K and H are 2 different subgroups of index 2. 
Now first prove $(H \cap K) \triangleleft G$ 
and then prove $\frac{G}{H \cap K}$ is not cyclic.
The first part went well (I used the fact that $H \triangleleft G$ and $K \triangleleft G$ because the indices of these subgroups are 2, the rest is quite easy). The second part however, didn't.

Thank you for your help!