  In a separate paper we have discussed the possibility that six quark clusters
can affect the rate of double-beta decay. In this article we develop the
formalism needed in the evaluation of the energy of all six-quark cluster
configurations, which can arise in a harmonic oscillator basis up to $2 \hbar
\omega$ excitations. The symmetries that were found useful for this purpose
were the combined spin color symmetry $SU_{cs}(6)$, the orbital symmetry
$SU_{o}(6)$ and the isospin symmetry $SU_I(2)$.
