  It is shown that the mechanism of order out of disorder is at work in the
antisymmetric pyrochlore antiferromagnet. Quantum as well as thermal
fluctuations break the continuous degeneracy of the classical ground state
manifold and reduce its symmetry to $\mathbb{Z}_3 \times \mathbb{Z}_2$. The
role of anisotropic symmetric exchange is also investigated and we conclude
that this discrete like ordering is robust with respect to these second order
like interactions. The antisymmetric pyrochlore antiferromagnet is therefore
expected to order at low temperatures, whatever the symmetry type of its
interactions, in both the classical and semi classical limits.
