Semiconductor nanowires became one of the most intensively studied system in quantum electronics in the last few years. With properly designed gate electrodes artificial atoms can be created in these nanowires. These can trap electrons which can store quantum information due to their spin. In this work the ground state of double quantum dot is studied in external magnetic field by inelastic co-tunnelling spectroscopy. The microscopic description of the system is complex due to the presence of strong spin-orbit interaction, spin-dependent tunneling and anisotropic Zeeman effect. However, we will show that using topological considerations one can formulate general predictions on the ground state of the system, which is verified by our measurements.