  We study the possibility of an intermediate scale existing in supersymmetric
E$_6$ grand unified theories. The intermediate scale is demanded to be around
$10^{12}$ GeV so that neutrinos can obtain masses suitable for explaining the
experimental data on the deficit of solar neutrinos with the
Mikheev-Smirnov-Wolfenstein solution and the existence of hot dark matter. We
require that at the intermediate scale, a certain symmetry breakdown to the
Standard Model symmetry. We show that only a few E$_6$ subgroups are likely to
be realized as the intermediate symmetry, though there are many candidates for
the intermediate symmetry in E$_6$ GUT.
