We report the first asteroseismic results obtained with the Hertzsprung Stellar Observations Network Group Telescope from an extensive high-precision radial-velocity observing campaign of the subgiant μ Herculis. The data set was collected during 215 nights in 2014 and 2015. We detected a total of 49 oscillation modes with l values from zero to three, including some l = 1 mixed modes. Based on the rotational splitting observed in l = 1 modes, we determine a rotational period of 52 days and a stellar inclination angle of 63°. The parameters obtained through modeling of the observed oscillation frequencies agree very well with independent observations and imply a stellar mass between 1.11 and 1.15 M ⊙ and an age of {7.8}-0.4+0.3 Gyr. Furthermore, the high-quality data allowed us to determine the acoustic depths of the He ii ionization layer and the base of the convection zone. Based on observations made with the Hertzsprung SONG telescope operated on the Spanish Observatorio del Teide on the island of Tenerife by the Aarhus and Copenhagen Universities and by the Instituto de Astrofísica de Canarias.