Normalizer of any subset of $S_n$

Question

Given any subset $S$ of $S_n$, can we find the normalizer of $S$ in $S_n$.

My thought:

1. $S$ can be partitioned in classes containing different cycle types, say $S=\cup_{i} \text Type\ (i)$. Now for each $\sigma \in N(S)$, $\sigma \text{Type(i)}\sigma^{-1}=\text{Type(i)}$. [As any to conjugate are of the same cycle-type]

I cannot proceed any further. Is there anything common between normalizers of any subset? Are there any results somehow connected to this? I have found a partial answer to the above question here.