I have $\displaystyle N_k$ is a normal subgroup of $\displaystyle K$ while $\displaystyle K$ is a normal subgroup of $\displaystyle G$.

i.e., $\displaystyle N_k \lhd K \lhd G$.

Is $\displaystyle N_k$ normal to $\displaystyle G$, i.e., $\displaystyle N_k \lhd G$ ? why?