  Monodisperse suspensions of Brownian colloidal spheres crystallize at high
densities, and ordering under shear has been observed at densities below the
crystallization threshold. We perform large-scale simulations of a model
suspension containing over $10^5$ particles to quantitatively study the
ordering under shear and to investigate its link to the rheological properties
of the suspension. We find that at high rates, for $Pe>1$, the shear flow
induces an ordering transition that significantly decreases the measured
viscosity. This ordering is analyzed in terms of the development of layering
and planar order, and we determine that particles are packed into hexagonal
crystal layers (with numerous defects) that slide past each other. By computing
local $\psi_6$ and $\psi_4$ order parameters, we determine that the defects
correspond to chains of particles in a square-like lattice. We compute the
individual particle contributions to the stress tensor and discover that the
largest contributors to the shear stress are primarily located in these lower
density, defect regions. The defect structure enables the formation of
compressed chains of particles to resist the shear, but these chains are
transient and short-lived. The inclusion of a contact friction force allows the
stress-bearing structures to grow into a system-spanning network, thereby
disrupting the order and drastically increasing the suspension viscosity.
