Natural convection in a cube of fluid-saturated porous medium heated from below and cooled from the top is studied numerically using a non-Darcy flow model. All vertical sidewalls are considered to be impermeable and adiabatic. The evolution of the various flow patterns is investigated from onset up to a Rayleigh number of 1000 where irregularly fluctuating convection prevails. New flow patterns have been found to exist in addition to those mentioned in the previous studies. In the present study, a total of ten steady flow patterns have been identified, of which five show oscillatory behaviour in some Rayleigh-number range. The results are presented in terms of average Nusselt number curves consisting of the solution branches of the convective patterns. The convective patterns are classified in terms of their symmetry properties, and the symmetries broken or gained during bifurcations from one flow structure to the other are identified.