  An abstract group $G$ is called totally $2$-closed if $H=H^{(2),\Omega}$ for
any set $\Omega$ with $G\cong H\leq{\rm Sym}(\Omega)$, where $H^{(2),\Omega}$
is the largest subgroup of ${\rm Sym}(\Omega)$ whose orbits on
$\Omega\times\Omega$ are the same orbits of $H$. In this paper, we classify the
finite soluble totally $2$-closed groups. We also prove that the Fitting
subgroup of a totally $2$-closed group is a totally $2$-closed group. Finally,
we prove that a finite insoluble totally $2$-closed group $G$ of minimal order
with non-trivial Fitting subgroup has shape $Z\cdot X$, with $Z=Z(G)$ cyclic,
and $X$ is a finite group with a unique minimal normal subgroup, which is
nonabelian.
