If $K$ is a Sylow p-subgroup of $G$ and $H$ is not normal in G, is $H\cap K$ a Sylow p-subgroup of $H$?

Question

If $K$ is a Sylow p-subgroup of $G$ and $H$ is not normal in G, is $H\cap K$ a Sylow p-subgroup of $H$?

I actually have no direction to answer this. So I tried several things that might not add up.

Since $H$ is not normal, it is not the unique Sylow p-subgroup of $G$ I also thought about The Second Sylow Theorem, that for $x \in G$ there exists $K=x^{-1}Hx$ and $H=x^{-1}Kx$, and that they are isomorphic to each other.

I may be way off.. Any help is appreciated.

Answer 1

Okay so look at groups of order $108$. If number of sylow $3$ subgroups is $4$,then those sylow $3$ subgroups are not normal. Take one of them H and one other K. Then $H \cap K$ is of order $3$ use $HK$ order formulae.So $H \cap K$ is not a sylow $3$ subgoup of $H$.