This question was asked in 
http://math.stackexchange.com/posts/729648/edit

Since I do not get any answer I asked it here.

In an answer in Mathoverflow I see an answer but I could not understand it. May anybody help me for Understanding it. The question and its answer are:

http://mathoverflow.net/questions/160427/on-the-character-degrees-of-a-finite-group-with-special-structure

In the beginning of the answer it is stated that by transfer and a theorem of Gaschutz we see that $N$ is complemented. By Gaschutz lemma (Stellmacher Page 74) we need an abelian and normal subgroup but $N$ is not abelian by assumption. could anybody explain why $N$ has a complement? 
Alex