Subgroups of Weil-Deligne group

Question

Let $K$ be a $p$-adic field, i.e. a finite extension of $\mathbb{Q}_p$. As I understand it, when studying Galois representations of $K$, in particualr $p$-adic ones, the "correct" thing to do is to study representations of the Weil-Deligne group $\text{WD}_K$. I'm wondering if there is a description of the closed subgroups of $\text{WD}_K$ in terms of certain field extensions of $K$ remeniscent of the bijection between closed subgroups of the absolute Galois group $G_K$ and Galois extensions of $K$?