We present here a comprehensive picture of the different bifurcations found for small to moderate Rayleigh number in binary-mixture convection with lateral heating and negative separation ratio (S). The present work connects the symmetric regime found for pure fluid (S=0)[Mercader et al 2005] with the fundamentally nonsymmetric regime found for S=-1 [Meca et al 2004a-2004b]. We give a global context as well as an interpretation for the different associations of bifurcations found, and in particular we interpret an association of codimension-two bifurcations in terms of a higher codimension bifurcation never found, to our knowledge, in the study of an extended system.