Multiple representation theories posit that concepts are represented via a combination of properties derived from sensorimotor, affective, and linguistic experiences. Recently, it has been proposed that information derived from social experience, or socialness, represents another key aspect of conceptual representation. How these various dimensions interact to form a coherent conceptual space has yet to be fully explored. To address this, we capitalized on openly available word property norms for 6339 words and conducted a large-scale investigation into the relationships between 18 dimensions. An exploratory factor analysis reduced the dimensions to six higher-order factors: sub-lexical, distributional, visuotactile, body action, affective and social interaction. All these factors explained unique variance in performance on lexical and semantic tasks, demonstrating that they make important contributions to the representation of word meaning. An important and novel finding was that the socialness dimension clustered with the auditory modality and with mouth and head actions. We suggest this reflects experiential learning from verbal interpersonal interactions. Moreover, formally modelling the network structure of semantic space revealed pairwise partial correlations between most dimensions and highlighted the centrality of the interoception dimension. Altogether, these findings provide new insights into the architecture of conceptual space, including the importance of inner and social experience, and highlight promising avenues for future research.