IsNormalSubXMod( X,Y )
A sub-crossed module Y=(N->M) is normal in X=(S->R) when
item N,M are normal subgroups of S,R respectively,
item n^r in N for all n in N, ; r in R,
item s^{-1} s^m in N for all m in M, ; s in S.
These axioms are sufficient to ensure that M semidirect N is a normal subgroup of R semidirect S. They also ensure that the inclusion morphism of a normal sub-crossed module forms a conjugation crossed square, analogous to the construction of a conjugation crossed module.
gap> IsNormalSubXMod( SX, subSX );
false
GAP 3.4.4