The hippocampus contributes to episodic, spatial and semantic aspects of memory, yet individual differences within and between these functions are not well-understood. In 136 healthy individuals, we investigated whether these differences reflect variation in the strength of connections between functionally-specialised segments of the hippocampus and diverse cortical regions that participate in different aspects of memory. Better topographical memory was associated with stronger connectivity between lingual gyrus and left anterior, rather than posterior, hippocampus. Better semantic memory was associated with increased connectivity between the intracalcarine/cuneus and left, rather than right, posterior hippocampus. Notably, we observed a double dissociation between semantic and topographical memory: better semantic memory was associated with stronger connectivity between left temporoparietal cortex and left anterior hippocampus, while better topographic memory was linked to stronger connectivity with right anterior hippocampus. Together these data support a division-of-labour account of hippocampal functioning: at the population level, differences in connectivity across the hippocampus reflect functional specialisation for different facets of memory, while variation in these connectivity patterns across individuals is associated with differences in the capacity to retrieve different types of information. In particular, within-hemisphere connectivity between hippocampus and left temporoparietal cortex supports conceptual processing at the expense of spatial ability.