I'm stuck on this problem. Hope someone can give me help.

Let H be a normal subgroup of G, show that if $\displaystyle x \in H$ then $\displaystyle ord(x^H)=ord(x^G)$ or $\displaystyle ord(x^H)=\frac{1}{2}ord(x^G)$

I think I need to construct an isomorphism, but I have no clue how to do it here.