  In this article, we show that a group $G$ is the union of two proper
subsemigroups if and only if $G$ has a nontrivial left-orderable quotient.
Furthermore, if $G$ is the union of two proper semigroups, then there exists a
minimum normal subgroup $N\unlhd G$ for which $G/N$ is left-orderable and
nontrivial.
