## What does it mean for a subgroup to be conjugate to another

Say in $S_3$ I let a subgroup, $H$, be generated by the permutation $(1,2)$. If I define another group, $C$ as $C=\{gHg^{-1} | g \in S_3\}$, $C$ is said to consist of all subgroups of $S_3$ that are conjugate to $H$. So this means I have to take every element in $S_3$ and conjugate it with all the elements in $H$ to know what the elements in C are? So I do $(1,2,3)(e,(1,2))(3,2,1)$, $(1,3,2)(e,(1,2))(2,3,1)$,... and so forth or does it mean something else?