Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
642 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 236 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14545753 | C2 | semidirect |
| 2. #14545176 | C2 | semidirect |
| 3. #14545173 | C2 | semidirect |
| 4. #14545125 | C2 | semidirect |
| 5. C2×#11763708 | C2 | semidirect |
| 6. #14544995 | C2 | semidirect |
| 9. #11763868 | C22 | semidirect |
| 14. #11763731 | C22 | semidirect |
| 15. #11763708 | C22 | semidirect |
| 16. #11763708 | C22 | semidirect |
| 17. #11763698 | C22 | semidirect |
| 18. #11763695 | C22 | semidirect |
| 175. C17 | #33442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545753 | 2 |
| #14545176 | 2 |
| #14545173 | 2 |
| #14545125 | 2 |
| C2×#11763708 | 2 |
| #14544995 | 2 |
| #14537686 | 2 |
| #33442 | 17 |