  We investigate phase coherent ballistic transport through antidot lattices in
the generic case where the classical phase space has both regular and chaotic
components. It is shown that the conductivity fluctuations have a non-Gaussian
distribution, and that their moments have a power-law dependence on a
semiclassical parameter, with fractional exponents. These exponents are
obtained from bifurcating periodic orbits in the semiclassical approximation.
They are universal in situations where sufficiently long orbits contribute.
