Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 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. #26042079 | C2 | semidirect |
| 2. C2×#19153842 | C2 | semidirect |
| 3. C2×#19153842 | C2 | semidirect |
| 4. #26042045 | C2 | semidirect |
| 5. #26041548 | C2 | semidirect |
| 6. #26041541 | C2 | semidirect |
| 7. #26041327 | C2 | semidirect |
| 8. #26041261 | C2 | semidirect |
| 9. C2×#100×C181 | C2 | semidirect |
| 13. #19153849 | C22 | semidirect |
| 15. #19153844 | C22 | semidirect |
| 22. C2×#15668437 | C22 | semidirect |
| 24. C2×#15668434 | C22 | semidirect |
| 25. #19153824 | C22 | semidirect |
| 30. #19153751 | C22 | semidirect |
| 31. #19153734 | C22 | semidirect |
| 32. #19153732 | C22 | semidirect |
| 36. #100×C181 | C22 | semidirect |
| 147. C181 | #3068 | semidirect |
| 157. C2×#100 | D181 | semidirect |
| 184. #100 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042079 | 2 |
| C2×#19153842 | 2 |
| #26042045 | 2 |
| #26041548 | 2 |
| #26041541 | 2 |
| #26041327 | 2 |
| #26041261 | 2 |
| C2×#100×C181 | 2 |
| #3068 | 181 |