I am looking for a group which satisfies the following conditions-
$1.$ $G \le U_1(\mathbb{Z}G)$ ,
where $U_1(\mathbb{Z}G)$ is the set of normalized units of $\mathbb{Z}G$ i.e. $U_1(\mathbb{Z}G)$ here means units of $\mathbb{Z}G$ with augmentation $1$, i.e. set of all elements $u=\sum_{g\in G} a(g)g \in U(\mathbb{Z}G)$ such that $\sum_{g \in G} a(g)=1$.
$2.$ [$U_1(\mathbb{Z}G):G] < \infty$
One example that I know is crystallographic groups. But what are some other examples.