Question generation (QG) task plays a crucial role in adaptive learning. While significant QG performance advancements are reported, the existing QG studies are still far from practical usage. One point that needs strengthening is to consider the generation of question group, which remains untouched. For forming a question group, intrafactors among generated questions should be considered. This article proposes a two-stage framework by combining neural language models and genetic algorithms for addressing the issue of question group generation. Furthermore, experimental evaluation based on benchmark datasets is conducted, and the results show that the proposed framework significantly outperforms the compared baselines. Human evaluations are also conducted to validate the design and understand the limitations.