We report a systematic study of longitudinal and transverse magnetoresistance in the quasi-one-dimensional organic conductor (TMTSF) 2 ClO 4 . We found two distinctly different quantum ͑rapid͒ oscillations ͑RO's͒ at different temperature regions in the field-induced spin-density-wave ͑FISDW͒ phase. For temperature sweeps in a fixed field, a resistance peak is observed at T* which depends on the field. Surprisingly, the type of RO is correlated with T*(H). The difference between two oscillations leads us to establish subphases in the main FISDW phase of (TMTSF) 2 ClO 4 . We also found the low-field boundary of McKernan's 3.5 K phase from a sudden increase of resistance. Our results conclude that the separate SDW transition on each pair of the Fermi surfaces is possibly responsible for subphases in the FISDW phase.