We present the results of a hierarchical Bayesian analysis of the morphologically dependent population star formation histories of group central and satellite galaxies in comparison to ​those in​ the field. To do this we utilise the classifications from Galaxy Zoo in a novel way, weighting by the vote fraction to include results from all galaxies rather than using a threshold to split our sample into late- and early-type morphology. We show that satellite galaxies on the outskirts of more massive groups have quenched more recently than galaxies in the inner regions and at a faster rate. This is statistically supported observational evidence for environmental quenching across the population due to satellite infall. As the mass of the group halo accumulates over time, the rate at which an infalling satellite can be quenched will therefore increase as the environmental density increases. We also correlate our findings with the presence of an AGN in both the satellite galaxies and group centrals.