There is John Dixon's book [Problems in Group Theory][1]. But I do not know whether you will classify it as graduate level or not. (It has the advantage that it is quite cheap.)  


  [1]: https://smile.amazon.co.uk/Problems-Group-Theory-Dover-Mathematics/dp/0486459160/ref=sr_1_2?dchild=1&keywords=dixon%20group%20theory&qid=1621425936&s=books&sr=1-2