The persistent current in three-dimensional (P×N2) nanorings as a function of the unit cell number (P), the channel number (M = N2), surface disorder (ξ), and temperature (T) is theoretically investigated in terms of rotational symmetry. On the whole, the typical current increases linearly with (<3) but decreases exponentially with P, while wide fluctuations exist therein. In the presence of surface disorder, the persistent current decreases with ξ in the regime of weak disorder but increases in the regime of strong disorder. In addition, it is found that the persistent current in perfect rings decreases exponentially with temperature even at T < T*, while in most disorder rings, the typical current decreases slightly with temperature at T < T*.