Humans are fundamentally social. They have progressively dominated their environment by the strength and creativity provided by and within their grouping. It is well recognised that human groups are highly structured, and the anthropological literature has loosely classified them according to their size and function, such as support cliques, sympathy groups, bands, cognitive groups, tribes, linguistic groups and so on. Recently, combining data on human grouping patterns in a comprehensive and systematic study, Zhou et al. identified a quantitative discrete hierarchy of group sizes with a preferred scaling ratio close to $3$, which was later confirmed for hunter-gatherer groups and for other mammalian societies. Using high precision large scale Internet-based social network data, we extend these early findings on a very large data set. We analyse the organisational structure of a complete, multi-relational, large social multiplex network of a human society consisting of about 400,000 odd players of a massive multiplayer online game for which we know all about the group memberships of every player. Remarkably, the online players exhibit the same type of structured hierarchical layers as the societies studied by anthropologists, where each of these layers is three to four times the size of the lower layer. Our findings suggest that the hierarchical organisation of human society is deeply nested in human psychology.