Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 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. C2×#19153863 | C2 | semidirect |
| 2. #26042079 | C2 | semidirect |
| 3. #26042077 | C2 | semidirect |
| 4. #26041855 | C2 | semidirect |
| 5. #26041463 | C2 | semidirect |
| 6. #26041453 | C2 | semidirect |
| 7. #26041297 | C2 | semidirect |
| 8. C2×#19153734 | C2 | semidirect |
| 9. #421×C181 | C2 | semidirect |
| 23. #19153849 | C22 | semidirect |
| 25. #19153846 | C22 | semidirect |
| 27. #19153844 | C22 | semidirect |
| 29. #19153841 | C22 | semidirect |
| 33. #19153816 | C22 | semidirect |
| 34. #19153804 | C22 | semidirect |
| 37. #19153744 | C22 | semidirect |
| 38. #19153734 | C22 | semidirect |
| 42. #104×C181 | C22 | semidirect |
| 185. C181 | #3020 | semidirect |
| 194. #421 | D181 | semidirect |
| 227. #104 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153863 | 2 |
| #26042079 | 2 |
| #26042077 | 2 |
| #26041855 | 2 |
| #26041463 | 2 |
| #26041453 | 2 |
| #26041297 | 2 |
| C2×#19153734 | 2 |
| #421×C181 | 2 |
| #3020 | 181 |