Methods of equivariant bifurcation theory are applied for investigation of Boussinesq convection in a plane layer with stress-free boundary conditions on horizontal boundaries and periodicity with the same period in $x$ and $y$ directions. We consider the problem near the onset of instability of the uniform conducting state where spatial roll patterns with two different wavelengths in the ratio $1:\sqrt2$ become simultaneuously unstable and give a mode interaction. Centre manifold reduction implies a normal form on $\C^4$ which is analysed both for arbitrary sets of coefficients and for particular values obtained by the reduction. The normal form predicts the appearence of robust heteroclinic networks involving steady states with different symmetries and robust attractors of generalised heteroclinic type that include connections from equilibria to subcycles; this is the first example of such a heteroclinic network in a fluid dynamical system that has `depth' greater than one. The normal form dynamics is in good correspondence (both quantatively and qualitatively) with direct numerical simulations of the full convection equations.