The complex quantum transport of a strained Ge quantum well (QW) modulation doped heterostructure with two types of mobile carriers has been observed. The two dimensional hole gas (2DHG) in the Ge QW exhibits an exceptionally high mobility of 780 000 cm2/Vs at temperatures below 10 K. Through analysis of Shubnikov de-Haas oscillations in the magnetoresistance of this 2DHG below 2 K, the hole effective mass is found to be 0.065 m0. Anomalous conductance peaks are observed at higher fields which deviate from standard Shubnikov de-Haas and quantum Hall effect behaviour due to conduction via multiple carrier types. Despite this complex behaviour, analysis using a transport model with two conductive channels explains this behaviour and allows key physical parameters such as the carrier effective mass, transport, and quantum lifetimes and conductivity of the electrically active layers to be extracted. This finding is important for electronic device applications, since inclusion of highly doped interlayers which are electrically active, for enhancement of, for example, room temperature carrier mobility, does not prevent analysis of quantum transport in a QW.