In the present study the existence of multiple three-dimensional double-diffusive flow patterns in a horizontal rectangular porous cavity of a square cross-section, having horizontal aspect ratios Ax = Ay = 2 is investigated numerically. Opposing vertical gradients of temperature and concentration are applied between the two horizontal walls of the cavity, where the solute gradient is destabilizing against a stabilizing temperature gradient. All vertical walls are considered to be impermeable and adiabatic. The Brinkman and Forchheimer terms are included in the momentum equations where the convective terms are retained. The effect of the buoyancy ratio, N, thermal Rayleigh number, RaT and Lewis number, Le, on the formation of multiple flow patterns is investigated over a wide range of parameters. Altogether 36 symmetric flow structures have been identified when each of the parameters N, RaT, and Le is varied independently, keeping the others as constants. The results of the calculations are presented in terms of the average Sherwood number curves consisting of different solution branches, where transitions between the branches are indicated. The flow patterns are classified according to their symmetry properties and the type of symmetries broken or preserved are identified during the bifurcation processes.