In this paper we study the stellar mass dependence of galaxy clustering in the 6dF Galaxy Survey (6dFGS). The near-infrared selection of 6dFGS allows more reliable stellar mass estimates compared to optical bands used in other galaxy surveys. Using the halo occupation distribution model, we investigate the trend of dark matter halo mass and satellite fraction with stellar mass by measuring the projected correlation function, wp(rp). We find that the typical halo mass (M1) as well as the satellite power-law index (α) increases with stellar mass. This indicates (1) that galaxies with higher stellar mass sit in more massive dark matter haloes and (2) that these more massive dark matter haloes accumulate satellites faster with growing mass compared to haloes occupied by low stellar mass galaxies. Furthermore, we find a relation between M1 and the minimum dark matter halo mass (Mmin) of M1 ≈ 22Mmin, in agreement with similar findings for Sloan Digital Sky Survey galaxies. The satellite fraction of 6dFGS galaxies declines with increasing stellar mass from 21 per cent at Mstellar=2.6×1010 h-2M⊙ to 12 per cent at Mstellar=5.4 × 1010 h-2M⊙ indicating that high stellar mass galaxies are more likely to be central galaxies. We compare our results to two different semi-analytic models derived from the Millennium Simulation, finding some disagreement. Our results can be used for placing new constraints on semi-analytic models in the future, particularly the behaviour of luminous red satellites. Finally, we compare our results to studies of halo occupation using galaxy-galaxy weak lensing. We find good overall agreement, representing a valuable cross-check for these two different tools of studying the matter distribution in the Universe.