The heavy ion synchrotron SIS100 is the main accelerator of the Facility for Antiproton and Ion Research project, which is located in Darmstadt, Germany. Within the four families of superconducting quadrupole doublet modules (QDMs), the development of the injection and extraction modules is the most demanding due to the complex configuration and the stringent position-stability requirements to be fulfilled. These modules are formed by two different beam branches, which have various components installed (e.g., focusing and defocusing main quadrupole (QP) magnets, low-current QP magnets, etc.). The positioning of the inner magnets is critical due to the maximum allowed transverse displacements relative to the ion optical lattice positions to be $\pm\!\!125 \mu\text{m}$ for the main QP magnets and $\pm 175 \mu\text{m}$ for the corrector magnets. The displacements allowed for the fiducial seats on the cryostat are $\pm 50 \mu\text{m}$ in all directions. The LHe cooling systems for the magnets and the ultrahigh vacuum components are formed by split circuit schemes for different beam branches in each module. All LHe pipes are conducted from the modules to adjacent cryogenic bypass lines. The thermomechanical design results in a unique challenge in terms of the development and mechanical integration of these QDMs.