Subgroups and normal-subgroups

Question

I have that $H$ is subgroup of a group $G$, and $K$ normal subgroup of a group $G$. I need to prove that $H\cap K$ is not a normal subgroup of $K$ if $G=K=S_3$ where $S_3$ are permutation with 3lines, and $H$ is generated with permutation (12)(3). I tried to prove that the order of $K$ is not divisible with the order of $H\cap K$, but i get nowhere with that.

Answer 1

HINT

$(13)(12)(13)^{-1}=(13)(12)(13)=(23)\not\in H\cap K$ hence $H\cap K$ is not normal in $G=S_3$