Shear-induced ordering is known to occur in sheared suspensions. The range of parameters for which this order occurs is probed here by simulation of monodisperse Brownian hard-sphere suspensions using accelerated Stokesian Dynamics. The simulations are performed for particle volume fractions of 0.47 <=phi <= 0.57 at Peclet numbers of 1 <= Pe=6 pi eta gamma a(3)/kT <= 10(4), where eta is the suspending fluid viscosity, gamma is the imposed shear rate, a is the sphere radius, and kT is the thermal energy. At Pe >= 10, when particle volume fraction is above phi approximate to 0.50, the suspensions undergo ordering over extended periods at the onset of flow, with remarkable reduction in the shear viscosity and self-diffusivity. The thixotropic response is a result of microstructural ordering, which is characterized both by the real space pair distribution function and its Fourier transform, the static structure factor. Both show that the particles tend to flow in chains with hexagonal packing in the plane normal to the flow. An order parameter is formulated to quantitatively describe the strength of this hexagonal packing. This ordering is not observed at Pe=1. Step changes in Pe are found to result in transitions of the structure and rheology. Hence the steady state rheology determined is uniquely associated with the flow conditions and particle fraction for most of the parameter space studied. However, near the boundary with respect to Pe between flow-induced order and disordered states of suspension at phi=0.55, the ultimate structure is history dependent within the typical simulation duration of material strain of O(100).