The problem of radar-based tracking of groups of people moving together and counting their numbers in indoor environments is considered here. A novel processing pipeline to track groups of people moving together and count their numbers is proposed and validated. The pipeline is specifically designed to deal with frequent changes of direction and stop & go movements typical of indoor activities. The proposed approach combines a tracker with a classifier to count the number of grouped people; this uses both spatial features extracted from range-azimuth maps, and Doppler frequency features extracted with wavelet decomposition. Thus, the pipeline outputs over time both the location and number of people present. The proposed approach is verified with experimental data collected with a 24 GHz Frequency Modulated Continuous Wave (FMCW) radar. It is shown that the proposed method achieves 95.59% accuracy in counting the number of people, and a tracking metric OSPA of 0.338. Furthermore, the performance is analyzed as a function of different relevant variables such as feature combinations and scenarios.