If $\displaystyle K\lhd G$ and $\displaystyle |g|=n$, $\displaystyle g\in G$, show that the order of $\displaystyle Kg$ in $\displaystyle G/K$ divides $\displaystyle n$.

So I know that $\displaystyle G=\{1,g,\cdots g^n\}$ and will $\displaystyle K=\{1,g, \cdots g^{n-1}\}$ ? From Lagrange's theorem K|G?

Thanks guys