What does it mean for a subgroup to be normal in another subgroup?

Question

I have a question of the form:

Assume $G$ is a group and $A$ and $B$ are subgroups with certain properties. Show that $A$ is normal in $B$.

I know normal would mean that $A \triangleleft G$ implies that $gAg^{-1} \subseteq A$ for all $g \in G$.

But what does it mean in this context?

Answer 1

It means $A \triangleleft B$, i.e. $A$ is normal when interpreted as a subgroup of $B$.

It makes sense only when $A \subseteq B$.