  I. Hambleton, L. Taylor and B. Williams conjectured a general formula in
spirit of H. Lenstra for the decomposition of $G_n(RG)$ for any finite group
$G$ and noetherian ring $R.$ The conjectured decomposition was shown to hold
for some large classes of finite groups. D. Webb and D. Yao discovered that the
conjecture failed for the symmetric group $S_5$, but remarked that it still
might be reasonable to expect the HTW-decomposition for solvable groups. In
this paper we show that the solvable group $\mathrm{SL}(2,\mathbb{F}_3)$ is
also a counterexample to the conjectured HTW-decomposition. Furthermore, we
prove that for any finite group $G$ the rank of $G_1(\mathbb{Z}G)$ does not
exceed the rank of the expression in the HTW-decomposition.
