deck transformations and covering spaces

Question

Let $p:\tilde X\rightarrow X$ be a universal covering space, and let $H\leq G$ where $G$ is the group of covering transformations. Let $q:\tilde X \rightarrow \tilde X/G$ be the quotient map which is regular covering space. Is $\tilde X/H\rightarrow X$ a covering space with appropriate map? If yes, what is this map?