Context. Gamma-ray bursts are usually classified in terms their high-energy emission into either short-duration or long-duration bursts, which presumably reflect two different types of progenitors. However, it has been shown on statistical grounds that a third, intermediate population is needed in this classification scheme, although an extensive study of the properties of this class has so far not been performed. The large amount of follow-up studies generated during the Swift era allows us to have a sufficient sample to attempt a study of this third population through the properties of their prompt emission and their afterglows. Aims. To understand the differences of the intermediate population, we study a sample of GRBs observed by Swift during its first four years of operation. The sample contains only bursts with measured redshifts since these data help us to derive intrinsic properties. Methods. We search for differences in the properties of the three groups of bursts, which we quantify using a Kolmogorov-Smirnov test whenever possible. Results. Intermediate bursts are found to be less energetic and have dimmer afterglows than long GRBs, especially when considering the X-ray light curves, which are on average one order of magnitude fainter than long bursts. There is a less significant trend in the redshift distribution that places intermediate bursts closer than long bursts. Except for this, intermediate bursts show similar properties to long bursts. In particular, they follow the E peak versus E iso correlation and have, on average, positive spectral lags with a distribution similar to that of long bursts. As for long GRBs, they normally have an associated supernova, although some intermediate bursts have been found to contain no supernova component. Conclusions. This study shows that intermediate bursts differ from short bursts, but exhibit no significant differences from long bursts apart from their lower brightness. We suggest that the physical difference between intermediate and long bursts could be explained by being produced by similar progenitors, of the former being the ejecta thin shells and the latter thick shells.