Analysis of the globular cluster (GC) system of the giant elliptical (E3) galaxy NGC 4365, from eightHubble Space Telescope/Advanced Camera for Surveys pointings and a wide-field Subaru/Suprime-Cam image, is presented. Using magnitude, colour and size criteria, we obtain a catalogue of GC candidates. We also measure the photometric properties of the galaxy starlight, including a new measure of the effective radius. We determine the lower limit on the number of GCs to beand show that the GC system extends beyond 134kpc (9.5 galaxy effective radii). We revisit the question of whether NGC 4365 has a bimodal or trimodal GC colour distribution and find support for three distinct GC colour subpopulations (i.e. blue, green and red). Sérsic profile fits to the radial surface density of each subpopulation reveal that the blue GCs are more extended than either the red or the green GCs. The median half-light radii for GCs in the blue, green and red subpopulations are,andpc, respectively. The estimated subpopulation ellipticities are, and for the blue, green and red GCs, respectively, where alignment with the photometric position angle of the galaxy is assumed. A Kolmogorov-Smirnov test on the mass functions shows a98per cent probability that all three subpopulations are distinct from one another. We also find radial gradients of GC size and colour (metallicity) and a blue tilt. The properties, including surface density profile, position angle, ellipticity and radial colour gradient, of the red GC subpopulation are very similar to the properties of NGC 4365's starlight. This result supports the hypothesis that red GCs are formed along with the bulk of the diffuse starlight in the galaxy. NGC 4365 has a kinematically distinct core and a significant misalignment between the photometric and kinematic major-axes. We discuss the possibility that these kinematic features are related to the presence of the distinct third GC subpopulation. We briefly discuss implications for the formation of NGC 4365, finding that major-merger, multiphase-collapse and accretion formation scenarios could all account for the existence of the third GC subpopulation.