  In this paper, we continue with the results in \cite{Pg} and compute the
group of quasi-isometries for a subclass of split solvable unimodular Lie
groups. Consequently, we show that any finitely generated group quasi-isometric
to a member of the subclass has to be polycyclic, and is virtually a lattice in
an abelian-by-abelian solvable Lie group. We also give an example of a
unimodular solvable Lie group that is not quasi-isometric to any finitely
generated group, as well deduce some quasi-isometric rigidity results.
