The clinical presentation of Alzheimer's disease (AD) varies widely across individuals but the neurobiological mechanisms underlying this heterogeneity are largely unknown. Here, we compared regional gray matter (GM) volumes and associated gene expression profiles between cognitively-defined subgroups of amyloid-β positive individuals clinically diagnosed with AD dementia (age: 66 ± 7, 47% male, MMSE: 21 ± 5). All participants underwent neuropsychological assessment with tests covering memory, executive-functioning, language and visuospatial-functioning domains. Subgroup classification was achieved using a psychometric framework that assesses which cognitive domain shows substantial relative impairment compared to the intra-individual average across domains, which yielded the following subgroups in our sample; AD-Memory (n = 41), AD-Executive (n = 117), AD-Language (n = 33), AD-Visuospatial (n = 171). We performed voxel-wise contrasts of GM volumes derived from 3Tesla structural MRI between subgroups and controls (n = 127, age 58 ± 9, 42% male, MMSE 29 ± 1), and observed that differences in regional GM volumes compared to controls closely matched the respective cognitive profiles. Specifically, we detected lower medial temporal lobe GM volumes in AD-Memory, lower fronto-parietal GM volumes in AD-Executive, asymmetric GM volumes in the temporal lobe (left < right) in AD-Language, and lower GM volumes in posterior areas in AD-Visuospatial. In order to examine possible biological drivers of these differences in regional GM volumes, we correlated subgroup-specific regional GM volumes to brain-wide gene expression profiles based on a stereotactic characterization of the transcriptional architecture of the human brain as provided by the Allen human brain atlas. Gene-set enrichment analyses revealed that variations in regional expression of genes involved in processes like mitochondrial respiration and metabolism of proteins were associated with patterns of regional GM volume across multiple subgroups. Other gene expression vs GM volume-associations were only detected in particular subgroups, e.g., genes involved in the cell cycle for AD-Memory, specific sets of genes related to protein metabolism in AD-Language, and genes associated with modification of gene expression in AD-Visuospatial. We conclude that cognitively-defined AD subgroups show neurobiological differences, and distinct biological pathways may be involved in the emergence of these differences.