Cell membranes are complex assemblies of lipids and proteins exhibiting lipid compositional heterogeneity between the inner and outer leaflets of the bilayer. Aberrant protein aggregation, implicated in a number of neurodegenerative diseases including Alzheimer's, is known to result in both extracellular and intracellular deposits with divergent pathophysiological effects. Mounting evidence substantiates membrane-mediated amyloid effects and indicates membrane composition, particularly gangliosides, as a plausible factor influencing the fibrillation process. By employing exhaustive molecular dynamics simulations using a coarse-grained model, we probed the assembly behavior of amyloidogenic Aβ(12-28) peptides on the chemically heterogeneous extracellular (outer) and cytosolic (inner) leaflets of a mammalian plasma membrane. Our results indicate that the compositional nature of the membrane has a crucial impact on the peptide self-assembly. Peptide oligomerization is hindered on the outer leaflet relative to the inner leaflet due to a competition between interpeptide and peptide-membrane interactions, resulting in higher population of smaller oligomers. The weaker associations among peptides on the outer membrane can be attributed to the favorable interactions of the peptides with gangliosides (GM) that characterize the extracellular membrane. At a higher peptide:GM ratio, we observe enhanced nanoclustering of GM lipids mediated by preferential GM-Aβ binding. Interaction between peptide and GM further impacts local membrane curvature; there is a concomitant loss in membrane concavity due to looser GM packing. Our simulations provide molecular insights into the role of membrane composition on Aβ aggregation and lend credence to earlier reports of ganglioside-mediated Aβ aggregation in the outer membrane. We also demonstrate the effects of local peptide assemblies on the membrane structure and dynamics.