Does the environment of a galaxy directly influence the quenching history of a galaxy ? Here we investigate the detailed morphological structures and star formation histories of a sample of SDSS group galaxies with both classifications from Galaxy Zoo 2 and NUV detections in GALEX . We use the optical and NUV colours to infer the quenching time and rate describing a simple exponentially declining SFH for each galaxy , along with a control sample of field galaxies . We find that the time since quenching and the rate of quenching do not correlate with the relative velocity of a satellite but are correlated with the group potential . This quenching occurs within an average quenching timescale of \sim 2.5 ~ { } Gyr from star forming to complete quiescence , during an average infall time ( from \sim 10 R _ { 200 } to 0.01 R _ { 200 } ) of \sim 2.6 ~ { } Gyr . Our results suggest that the environment does play a direct role in galaxy quenching through quenching mechanisms which are correlated with the group potential , such as harassment , interactions or starvation . Environmental quenching mechanisms which are correlated with satellite velocity , such as ram pressure stripping , are not the main cause of quenching in the group environment . We find that no single mechanism dominates over another , except in the most extreme environments or masses . Instead an interplay of mergers , mass & morphological quenching and environment driven quenching mechanisms dependent on the group potential drive galaxy evolution in groups .