Here, we compare the sunspot counts and the number of sunspot groups (SGs) with variations of total solar irradiance (TSI), magnetic activity, Ca II K-flux, faculae and plage areas. We applied a time series method for extracting the data over the descending phases of solar activity cycles (SACs) 21, 22 and 23, and the ascending phases 22 and 23. Our results suggest that there is a strong correlation between solar activity indices and the changes in small (A, B, C and H-modified Zurich Classification) and large (D, E and F) SGs. This somewhat unexpected finding suggests that plage regions substantially decreased in spite of the higher number of large SGs in SAC 23 while the Ca II K-flux did not decrease by a large amount nor was it comparable with SAC 22 and relates with C and DEF type SGs. In addition to this, the increase of facular areas which are influenced by large SGs, caused a small percentage decrease in TSI while the decrement of plage areas triggered a higher decrease in the magnetic field flux. Our results thus reveal the potential of such a detailed comparison of the SG analysis with solar activity indices for better understanding and predicting future trends in the SACs.