ABSTRACT Cosmic filaments are the channel through which galaxy groups assemble their mass. Cosmic connectivity, namely the number of filaments connected to a given group, is therefore expected to be an important ingredient in shaping group properties. The local connectivity is measured in COSMOS around X-ray-detected groups between redshift 0.5 and 1.2. To this end, large-scale filaments are extracted using the accurate photometric redshifts of the COSMOS2015 catalogue in two-dimensional slices of thickness 120 comoving Mpc centred on the group’s redshift. The link between connectivity, group mass, and the properties of the brightest group galaxy (BGG) is investigated. The same measurement is carried out on mocks extracted from the light-cone of the hydrodynamical simulation Horizon-AGN in order to control systematics. More massive groups are on average more connected. At fixed group mass in low-mass groups, BGG mass is slightly enhanced at high connectivity, while in high-mass groups BGG mass is lower at higher connectivity. Groups with a star-forming BGG have on average a lower connectivity at given mass. From the analysis of the Horizon-AGN simulation, we postulate that different connectivities trace different paths of group mass assembly: at high group mass, groups with higher connectivity are more likely to have grown through a recent major merger, which might be in turn the reason for the quenching of the BGG. Future large-field photometric surveys, such as Euclid and LSST, will be able to confirm and extend these results by probing a wider mass range and a larger variety of environment.