We have detected several periodicities in the solar equatorial rotation rate of sunspot groups in the catalog Greenwich Photoheliographic Results (GPR) during the period 1931 – 1976, the Solar Optical Observing Network (SOON) during the period 1977 – 2014, and the Debrecen Photoheliographic Data (DPD) during the period 1974 – 2014. We have compared the results from the fast Fourier transform (FFT), the maximum entropy method (MEM), and the Morlet wavelet power-spectra of the equatorial rotation rates determined from SOON and DPD sunspot-group data during the period 1986 – 2007 with those of the Mount Wilson Doppler-velocity data during the same period determined by Javaraiah et al. ( Solar Phys. 257 , 61, 2009 ). We have also compared the power-spectra computed from the DPD and the combined GPR and SOON sunspot-group data during the period 1974 – 2014 to those from the GPR sunspot-group data during the period 1931 – 1973. Our results suggest a ∼ 250-day period in the equatorial rotation rate determined from both the Mt. Wilson Doppler-velocity data and the sunspot-group data during 1986 – 2007. However, a wavelet analysis reveals that this periodicity appears mostly around 1991 in the velocity data, while it is present in most of the solar cycles covered by the sunspot-group data, mainly near the minimum epochs of the solar cycles. We also found the signature of a period of ∼ 1.4 years in the velocity data during 1990 – 1995, and in the equatorial rotation rate of sunspot groups mostly around the year 1956. The equatorial rotation rate of sunspot groups reveals a strong ∼ 1.6-year periodicity around 1933 and 1955, a weaker one around 1976, and a strong ∼ 1.8-year periodicity around 1943. Our analysis also suggests periodicities of ∼ 5 years, ∼ 7 years, and ∼ 17 years, as well as some other short-term periodicities. However, short-term periodicities are mostly present at the time of solar minima. Hence, short-term periodicities cannot be confirmed because of the larger uncertainty in the data.