[Norton and Wilson - Maximal subgroups of the Harada–Norton group](https://doi.org/10.1016/0021-8693(86)90192-4) seems to imply that $HN \rtimes C_2$ works, along with its overgroups $\mathbb{B}$ and $\mathbb{M}$.


  [1]: https://www.sciencedirect.com/science/article/pii/0021869386901924