Based on SDSS galaxy sample, we identify a clear transition feature of galaxy quenching in the multi-parameter space of stellar mass(M*), bulge to total mass ratio (B/T), halo mass(Mh) and halo-centric distance(r/r180). For given halo mass, the characteristic stellar mass (Mch) for the transition is about one-fifth of that of the corresponding central galaxy, and almost independent of galaxy morphology. Once B/T is fixed, the quenched fraction of galaxies with M*<Mch increases with halo mass, but decreases with stellar mass in the inner part of halos (r/r180<0.5). In the outer part (r/r180>0.5), the trend with halo mass remains but the correlation with stellar mass is absent or becomes positive. For galaxies above Mch and with B/T fixed, the quenched fraction increases with stellar mass, but depends only weakly on halo mass in both the inner and outer regions. At fixed B/T and M*, the quenched fraction increases with decreasing r/r180 for galaxies with M*<Mch, and is almost independent r/r180 for galaxies with M*>Mch. Our finding provides a physically-motivated way to classify galaxies in halos into two classes based on their quenching properties: an `upper class' with M*>Mch} and a `lower class' with M*<Mch$. Environmental quenching is important only for `lower class' galaxies, while internal quenching plays the dominating role for the `upper class'.
