Conjugate subgroups are in bijection with cosets of normalizer

Statement
Suppose $$H$$ is a subgroup of a group $$G$$. Then, there is a natural bijection between the following two sets:


 * 1) The coset space of the normalizer of $$H$$ in $$G$$, i.e., the space $$G/N_G(H)$$
 * 2) The set of conjugate subgroups to $$H$$ in $$G$$, i.e. the conjugacy class of subgroups of $$G$$, that has $$H$$

(Note that it doesn't matter whether we take the left or right coset spaces, because the left and right coset spaces are naturally isomorphic).