Construction of Covering space by Galois correspondence

Question

We know, If $X$ is path connected,locally pathconnected,semi locally simply connected then $X$ has a universal cover $\overline X$.Now, By Galois Correspondence for any subgroup $H$ of $π_{1}(X)$ we can find subcover $X_H$ of $\overline X$ such that $p_*(X_H)=H$. My Question is : If I know universal cover ,Can I explicitly find $X_H$ for any $H$ ??