Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
454 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26041813 | C2 | semidirect |
| 2. C2×C4×D724 | C2 | semidirect |
| 3. #26041615 | C2 | semidirect |
| 4. #26041598 | C2 | semidirect |
| 5. #26041580 | C2 | semidirect |
| 6. #26041495 | C2 | semidirect |
| 7. #26041432 | C2 | semidirect |
| 9. C4×#15668438 | C2 | semidirect |
| 10. C4×D1448 | C2 | semidirect |
| 11. #431×C181 | C2 | semidirect |
| 17. #19153808 | C22 | semidirect |
| 18. #19153804 | C22 | semidirect |
| 22. C4×Dic362 | C22 | semidirect |
| 27. C4×D724 | C22 | semidirect |
| 32. #19153750 | C22 | semidirect |
| 33. #19153748 | C22 | semidirect |
| 34. #19153741 | C22 | semidirect |
| 37. #19153738 | C22 | semidirect |
| 39. C4⋊C8×C181 | C22 | semidirect |
| 42. C4×C8×C181 | C22 | semidirect |
| 140. C181 | #3105 | semidirect |
| 152. #431 | D181 | semidirect |
| 176. C4⋊C8 | C2×D181 | semidirect |
| 183. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041813 | 2 |
| C2×C4×D724 | 2 |
| #26041615 | 2 |
| #26041598 | 2 |
| #26041580 | 2 |
| #26041495 | 2 |
| #26041432 | 2 |
| #26041415 | 2 |
| C4×#15668438 | 2 |
| C4×D1448 | 2 |
| #431×C181 | 2 |
| #3105 | 181 |