Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26042003 | C2 | semidirect |
| 2. #26041999 | C2 | semidirect |
| 4. #26041658 | C2 | semidirect |
| 5. #26041504 | C2 | semidirect |
| 6. #26041499 | C2 | semidirect |
| 7. #26041485 | C2 | semidirect |
| 8. #26041403 | C2 | semidirect |
| 9. #26041371 | C2 | semidirect |
| 11. #461×C181 | C2 | semidirect |
| 123. C181 | #3393 | semidirect |
| 132. #461 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042003 | 2 |
| #26041999 | 2 |
| #26041660 | 2 |
| #26041658 | 2 |
| #26041504 | 2 |
| #26041499 | 2 |
| #26041485 | 2 |
| #26041403 | 2 |
| #26041371 | 2 |
| C4×#15668434 | 2 |
| #461×C181 | 2 |
| #3393 | 181 |