# Existence of a subgroup of a certain order

Suppose a group $G$ with $|G|=162$ has a normal subgroup $K$ with $|K|=9$. Show that $G$ must have a subgroup of order 18, using $HK/K \cong H/(K \cap H)$.

I feel like this should be very easy, and my ongoing failure to do it is beginning to make me really resent mathematics.

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Notice first that $G$ has some subgroup $H$ of order $2$. Then show that $HK$ has order $18$.