We report the discovery that substructures/subhaloes of a galaxy-size halo tend to fall in together in groups in cosmological simulations, something that may explain the oddity of the MW satellite distribution. The original clustering at the time of infall is still discernible in the angular momenta of the subhaloes even for events which took place up to eight Gyrs ago, z ~ 1. This phenomenon appears to be rather common since at least 1/3 of the present-day subhaloes have fallen in groups in our simulations. Hence, this may well explain the Lynden-Bell & Lynden-Bell ghostly streams. We have also found that the probability of building up a flattened distribution similar to the MW satellites is as high as ~ 80% if the MW satellites were from only one group and ~ 20% when five groups are involved. Therefore, we conclude that the ‘peculiar’ distribution of satellites around the MW can be expected with the CDM structure formation theory. This non-random assignment of satellites to subhaloes implies an environmental dependence on whether these low-mass objects are able to form stars, possibly related to the nature of reionization in the early Universe.