The concept of a group is ubiquitous in biology. It underlies classifications in evolution and ecology, including those used to describe phylogenetic levels, the habitat and functional roles of organisms in ecosystems. Surprisingly, this concept is not explicitly included in simple models for the structure of food webs, the ecological networks formed by consumer-resource interactions. We present here the simplest possible model based on groups, and show that it performs substantially better than current models at predicting the structure of large food webs. Our group-based model can be applied to different types of biological and non-biological networks, and for the first time merges in the same framework two important notions in network theory: that of compartments (sets of highly interacting nodes) and that of roles (sets of nodes that have similar interaction patterns). This model provides a basis to examine the significance of groups in biological networks and to develop more accurate models for ecological network structure. It is especially relevant at a time when a new generation of empirical data is providing increasingly large food webs.