Spin-orbit interaction and spd exchange interaction are investigated by analyzing beating patterns of Shubnikov-de Hass oscillations in a HgMnTe magnetic two-dimensional electron gas (2DEG) at various temperatures.The results show that (1) spin-orbit interaction results in zero-magnetic-field spin splitting in 2DEG; (2) spin-orbit interaction is dominant at low magnetic field, and the total spin-splitting decreases with increasing magnetic field due to the influence of Landau splitting and Zeeman splitting; (3) at a high magnetic field, the spd exchange interaction tends to saturate and the spin splitting corresponds to Zeeman splitting. The experiments demonstrate that the spin splitting deduced from fast Fourier transformation (FFT) of SdH oscillations versus. 1/B is different from zero-magnetic-field spin splitting when Zeeman spin splitting is comparable to zero-magnetic-field spin splitting.