The mental lexicon stores words and information about words. The lexicon is seen by many researchers as a network, where lexical units are nodes and the different links between the units are connections. Based on the analysis of a word association network, in this article we show that different kinds of associative connections exist in the mental lexicon. Our analysis is based on a word association database from the agglutinative language Hungarian. We use communities - closely knit groups - of the lexicon to provide evidence for the existence and coexistence of different connections. We search for communities in the database using two different algorithms, enabling us to see the overlapping (a word belongs to multiple communities) and non-overlapping (a word belongs to only one community) community structures. Our results show that the network of the lexicon is organized by semantic, phonetic, syntactic and grammatical connections, but encyclopedic knowledge and individual experiences are also shaping the associative structure. We also show that words may be connected not just by one, but more types of connections at the same time.