  We prove that for all $k,m,n \in \mathbb N \cup \{\infty\}$ with $4 \leq k
\leq m \leq n$, there exists a finitely generated group $G$ with a finitely
generated subgroup $H$ such that the asymptotic dimension of $G$ is $k$, the
Assouad-Nagata dimension of $G$ is $m$, and the Assouad-Nagata dimension of $H$
is $n$. This simultaneously answers two open questions in asymptotic dimension
theory.
