Well-motivated elementary particle candidates for the dark matter, such as the sterile neutrino, behave as warm dark matter (WDM). For particle masses of the order of a keV, free streaming produces a cutoff in the linear fluctuation power spectrum at a scale corresponding to dwarf galaxies. We investigate the abundance and structure of WDM haloes and subhaloes on these scales using high resolution cosmological N-body simulations of galactic haloes of mass similar to the Milky Way's. On scales larger than the free-streaming cutoff, the initial conditions have the same power spectrum and phases as one of the cold dark matter (CDM) haloes previously simulated by Springel et al. as part of the Virgo consortium Aquarius project. We have simulated four haloes with WDM particle masses in the range 1.5–2.3 keV and, for one case, we have carried out further simulations at varying resolution. N-body simulations in which the power spectrum cutoff is resolved are known to undergo artificial fragmentation in filaments producing spurious clumps which, for small masses (