  We study a model for pair interaction $U$ of DNA molecules generated by the
discrete dipole moments of base-pairs and the charges of phosphate groups, and
find noncommutative group of eighth order ${\cal S}$ of symmetries that leave
$U$ invariant. We classify the minima using group ${\cal S}$ and employ
numerical methods for finding them. The minima may correspond to several
cholesteric phases, as well as phases formed by cross-like conformations of
molecules at an angle close to $\rm{90}^{o}$, "snowflake phase". The results
depend on the effective charge $Q$ of the phosphate group which can be modified
by the polycations or the ions of metals. The snowflake phase could exist for
$Q$ above the threshold $Q_C$. Below $Q_C$ there could be several cholesteric
phases. Close to $Q_C$ the snowflake phase could change into the cholesteric
one at constant distance between adjacent molecules.
