# Irregular covering of 2-holed torus $S_2$

I need to find an irregular covering of the 2-holed torus. If a covering is regular, then $$p_*(\pi_1(E,e_0))$$ is a normal subgroup of $$\pi_1(S_2,b_0)$$, where $$E$$ denotes the covering space. So an irregular covering would not have this property. I was thinking if $$E=S_2$$ (which is just itself) is such a covering, but I don't know why or how to justify it. If the trivial covering is regular, then what would be an (easily understood) irregular covering of $$S_2$$? Thanks!