  Two isometry groups of combinatorial codes are described: the group of
automorphisms and the group of monomial automorphisms, which is the group of
those automorphisms that extend to monomial maps. Unlike the case of classical
linear codes, where these groups are the same, it is shown that for
combinatorial codes the groups can be arbitrary different. Particularly, there
exist codes with the full automorphism group and the trivial monomial
automorphism group. In the paper the two groups are characterized and codes
with predefined isometry groups are constructed.
