  We establish explicit formulae for canonical factorizations of extended
solutions corresponding to harmonic maps of finite uniton number into the
exceptional Lie group $G_2$ in terms of the Grassmannian model for the group of
based algebraic loops in $G_2$. A description of the ``Frenet frame data" for
such harmonic maps is given. In particular, we show that harmonic spheres into
$G_2$ correspond to solutions of certain algebraic systems of quadratic and
cubic equations.
