  We extend the nonabelian Dold-Kan decomposition for simplicial groups of
Carrasco and Cegarra in two ways. First, we show that the total order of the
subgroups in their decomposition belongs to a family of total orders all giving
rise to Dold-Kan decompositions. We exhibit a particular partial order such
that the family is characterized as consisting of all total orders extending
the partial order. Second, we consider symmetric-simplicial groups and show
that, by using a specially chosen presentation of the category of
symmetric-simplicial operators, new Dold-Kan decompositions exist which are
algebraically much simpler than those of Carrasco and Cegarra in the sense that
the commutator of two component subgroups lies in a single component subgroup.
