Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
430 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041950 | C2 | semidirect |
| 2. #26041627 | C2 | semidirect |
| 3. #26041597 | C2 | semidirect |
| 4. #26041561 | C2 | semidirect |
| 5. #26041530 | C2 | semidirect |
| 6. #26041474 | C2 | semidirect |
| 7. #26041422 | C2 | semidirect |
| 8. C4×#15668437 | C2 | semidirect |
| 9. #26041357 | C2 | semidirect |
| 10. #26041278 | C2 | semidirect |
| 11. #547×C181 | C2 | semidirect |
| 79. Dic362 | #41 | semidirect |
| 134. C181 | #3332 | semidirect |
| 137. #547 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041950 | 2 |
| #26041627 | 2 |
| #26041597 | 2 |
| #26041561 | 2 |
| #26041530 | 2 |
| #26041474 | 2 |
| #26041422 | 2 |
| C4×#15668437 | 2 |
| #26041357 | 2 |
| #26041278 | 2 |
| #547×C181 | 2 |
| #3332 | 181 |