Multicast beamforming is known to improve spectral efficiency. However, its benefits and challenges for hybrid precoders design in millimeter-wave (mmWave) systems remain understudied. To this end, this paper investigates the first joint design of hybrid transmit precoders (with an arbitrary number of finite-resolution phase shifts) and receive combiners for mmWave multi-group multicasting. Our proposed design leverages semidefinite relaxation (SDR), alternating optimization and Cholesky matrix factorization to sequentially optimize the digital/analog precoders at the transmitter and the combiners at each receiver. By considering receivers with multiple-antenna architecture, our design remarkably improves the overall system performance. Specifically, with only two receive antennas the average transmit power per received message improves by $ 16.8\% $ while the successful information reception is boosted by $ 60\% $. We demonstrate by means of extensive simulations that our hybrid precoder design performs very close to its fully-digital counterpart even under challenging scenarios (i.e., when co-located users belong to distinct multicast groups).