Find all Galois extensions of degree 6 of $K=\mathbb{C}(S,T,U)$

Question

Let $K=\mathbb{C}(S,T,U)$ be the rational function field over the complex field and $L$ be the splitting field of $F(x)=x^6-Sx^4+Tx^2-U\in K[X]$. Find $[L:K]$ and all the Galois extensions of degree $6$ of $K$ contained in $L$.

I have no idea. What should I do first?