Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19153836 | C2 | semidirect |
| 2. C22×#15668432 | C2 | semidirect |
| 3. #26041791 | C2 | semidirect |
| 4. #26041786 | C2 | semidirect |
| 5. #26041536 | C2 | semidirect |
| 6. #26041531 | C2 | semidirect |
| 7. #26041528 | C2 | semidirect |
| 8. #26041524 | C2 | semidirect |
| 9. #26041315 | C2 | semidirect |
| 10. #26041276 | C2 | semidirect |
| 11. #416×C181 | C2 | semidirect |
| 15. C2×#15668439 | C22 | semidirect |
| 16. C2×#15668437 | C22 | semidirect |
| 17. C2×#15668436 | C22 | semidirect |
| 18. C2×#15668434 | C22 | semidirect |
| 34. #19153749 | C22 | semidirect |
| 35. #19153747 | C22 | semidirect |
| 36. #19153741 | C22 | semidirect |
| 37. #19153738 | C22 | semidirect |
| 41. #103×C181 | C22 | semidirect |
| 42. #102×C181 | C22 | semidirect |
| 63. C2×#13089678 | D4 | semidirect |
| 148. C181 | #3054 | semidirect |
| 160. #416 | D181 | semidirect |
| 189. #103 | C2×D181 | semidirect |
| 191. #102 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153836 | 2 |
| C22×#15668432 | 2 |
| #26041791 | 2 |
| #26041786 | 2 |
| #26041536 | 2 |
| #26041531 | 2 |
| #26041528 | 2 |
| #26041524 | 2 |
| #26041315 | 2 |
| #26041276 | 2 |
| #416×C181 | 2 |
| #3054 | 181 |