In this work, we report the synthesis as well as the structural and magnetic characterization of the three perovskites La2MnB'O6 (B' = Ti, Zr, and Hf). Interestingly, only La2MnTiO6 crystallizes in the monoclinic double perovskite space group P21/n, with a complete rocksalt order of the B-site cations, whereas La2MnZrO6 and La2MnHfO6 crystallize in the orthorhombic simple perovskite space group Pbnm, with complete disorder in the B site. Moreover, the magnetic susceptibility at low temperatures shows clear antiferromagnetic transitions below 10 K for the three compounds, but only the Ti-based perovskite has long-range magnetic ordering. The latter compound has an antiferromagnetic type-II structure described by the PS-1 magnetic space group, while the other two have a spin-glass behavior below the transition temperature due to both spin disorder and competing superexchange interactions in the systems. This is the first time that two of the three studied compounds were synthesized (B' = Zr and Hf) and the first time that the whole series is described in thorough detail using symmetry-adapted refinements and magnetic crystallography.