Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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. #26042077 | C2 | semidirect |
| 2. C2×#19153844 | C2 | semidirect |
| 3. C2×#19153841 | C2 | semidirect |
| 4. #26041549 | C2 | semidirect |
| 5. #26041542 | C2 | semidirect |
| 6. #26041328 | C2 | semidirect |
| 7. #26041261 | C2 | semidirect |
| 8. C2×#19153732 | C2 | semidirect |
| 9. #568×C181 | C2 | semidirect |
| 13. #19153846 | C22 | semidirect |
| 19. #19153841 | C22 | semidirect |
| 21. C2×#15668438 | C22 | semidirect |
| 23. C2×D1448 | C22 | semidirect |
| 27. #19153752 | C22 | semidirect |
| 28. #19153734 | C22 | semidirect |
| 29. #19153732 | C22 | semidirect |
| 30. #19153732 | C22 | semidirect |
| 33. #131×C181 | C22 | semidirect |
| 147. C181 | #3068 | semidirect |
| 152. #568 | D181 | semidirect |
| 175. #131 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042077 | 2 |
| C2×#19153844 | 2 |
| C2×#19153841 | 2 |
| #26041549 | 2 |
| #26041542 | 2 |
| #26041328 | 2 |
| #26041261 | 2 |
| C2×#19153732 | 2 |
| #568×C181 | 2 |
| #3068 | 181 |