While studying Groups from Thomas Hungerford I was unable to understand reasoning behind a deduction in a proof on page104.
Adding it's image:
Question: How does in line 3 of proof of (iii) solvability of $N$ implies $N'\neq N $ and $N$ is abelian.
Note : Minimal Normal Subgroup: It is a non trivial normal subgroup of group $G$ that contains no proper subgroup which is normal in $G.$
Theorem 7.11
(I) Every subgroup and every homeomorphic image of solvable group is solvable.
(II) If $N$ is a normal subgroup of $G$ such that $N$ and $G/N$ are solvable, then $G$ is solvable.
Kindly help.