Magnesium is one of the important elements in stellar physics as an electron donor and in Galactic Archaeology as a discriminator of different stellar populations. However, previous studies of Mgi and Mgii lines in metal-poor benchmark stars have flagged problems with magnesium abundances inferred from one-dimensional (1D), hydrostatic models of stellar atmospheres, both with or without the local thermodynamic equilibrium (LTE) approximation.We here present 3D non-LTE calculations for magnesium in FG-type dwarfs, and provide corrections for 1D LTE abundances. The 3D non-LTE corrections reduce the ionisation imbalances in the benchmark metal-poor stars HD84937 and HD140283 from -0.16dex and -0.27dex in 1D LTE, to just -0.02dex and -0.09dex respectively.We then applied our abundance corrections to 1D LTE literature results for stars in the thin disc, thick disc, alpha-rich halo, and alpha-poor halo. We find that the 3D non-LTE results show a richer substructure in [Mg/Fe]-[Fe/H] in the alpha-poor halo, revealing two subpopulations at the metal-rich end. These two subpopulations are also separated in kinematics, supporting the astrophysical origin of the separation. While the more magnesium-poor subpopulation is likely to be debris from a massive accreted galaxy, Gaia-Enceladus, the other subpopulation may be related to a previous identified group of stars, called Eos. The presence of additional separation in [Mg/Fe] suggests that previous Mg abundance measurements may have been limited in the precision by the 1D and LTE approximations, highlighting the importance of 3D non-LTE modelling.