# group theory – Show \$(Gtimes H)/(Ktimes K’) cong G/Ktimes H/K’\$ if \$Klhd G\$ and \$K’lhd H\$

As the title says, I want to show that $$(Gtimes H)/(Ktimes K’) cong G/Ktimes H/K’$$ if $$Klhd G$$ and $$K’lhd H$$.

I already showed that $$Ktimes K’$$ is a normal subgroup of $$Gtimes H$$ and I think that I should use the isomorphism theorem stating that if $$A,B$$ are groups and $$f:Ato B$$ is a homomorphism then $$f(A)=A/text{ker}(f)$$. But I can’t figure out how to go further. Can you help me to prove this problem?