  Let $G$ be a finite group and let $\pi: G \to G'$ be a surjective group
homomorphism. Consider the cocycle deformation $L = H^{\sigma}$ of the Hopf
algebra $H = k^G$ of $k$-valued linear functions on $G$, with respect to some
convolution invertible 2-cocycle $\sigma$. The (normal) Hopf subalgebra $k^{G'}
\subseteq k^G$ corresponds to a Hopf subalgebra $L' \subseteq L$. Our main
result is an explicit necessary and sufficient condition for the normality of
$L'$ in $L$.
