My question is connected (pun intended) to the Exercise 1.3.14 of Allen Hatcher's Algebraic Topology.
The question is to find all connected covering spaces of $\mathbb RP^2\vee \mathbb RP^2.$ I understand how to solve the problem by first finding the fundamental group of $\mathbb RP^2\vee \mathbb RP^2$ and then computing the covers corresponding to the subgroups of the fundamental group. This provides a detailed solution as of how to find the connected covering spaces.
My question is this: how do we find the covering spaces of $\mathbb RP^2\vee \mathbb RP^2.$ that are not connected? Are there any general techniques or methods that can be used to answer this question?
Thank you!