I've found the following theorem in "Topology" by Klaus Janich, chapter 7, but left without proof. I have no idea how to begin, and could not find any sketch of proof of this thm neither in literature nor internet.
Let $X$ be a path-connected, locally path-connected and semi-locally simply connected space, let $x_0 \in X$, and let $(Y, y_0)\rightarrow (X, x_0)$ be the universal cover and $\mathcal{D}_X \cong \pi_1 (X,x_0)$ the group of covering transformations of $Y \rightarrow X$. Then if $\Gamma \subset \mathcal{D}_X$ is an arbitrary subgroup, the map $(Y/\Gamma, [y_0]) \rightarrow (X,x_0)$ is the covering map of a path-connected covering space and all path-connected covering spaces of $(X,x_0)$ are obtained in this way, up to uniquely determined isomorphism.