Suppose $G$ is a finite group and $N_1, N_2, \cdots, N_k$ are proper normal subgroups of $G$. The set $\{ N_1, \cdots, N_k\}$ is called a normal cover for $G$, if $G = \cup_{i=1}^kN_i$. I need to the main properties of finite groups with a normal covering. Anybody knows some references on this topic. There are several published papers on covering of groups by subgroups, but I like normal cover. Any comments will be highly appreciated.

Sincerely, F Moftakhar