  We classify Fano threefolds with only terminal singularities whose canonical
class is Cartier and divisible by 2, and satisfying an additional assumption
that the $G$-invariant part of the Weil divisor class group is of rank 1 with
respect to an action of some group $G$. In particular, we find a lot of
examples of Fano 3-folds with "many" symmetries.
