Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
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. #26012291 | C2 | semidirect |
| 2. C2×#19149705 | C2 | semidirect |
| 3. C2×#19149705 | C2 | semidirect |
| 4. #26012257 | C2 | semidirect |
| 5. #26011760 | C2 | semidirect |
| 6. #26011753 | C2 | semidirect |
| 7. #26011539 | C2 | semidirect |
| 8. #26011473 | C2 | semidirect |
| 9. C2×#100×C173 | C2 | semidirect |
| 13. #19149712 | C22 | semidirect |
| 15. #19149707 | C22 | semidirect |
| 22. C2×#14583814 | C22 | semidirect |
| 24. C2×#14583811 | C22 | semidirect |
| 25. #19149687 | C22 | semidirect |
| 30. #19149614 | C22 | semidirect |
| 31. #19149597 | C22 | semidirect |
| 32. #19149595 | C22 | semidirect |
| 36. #100×C173 | C22 | semidirect |
| 147. C173 | #3068 | semidirect |
| 157. C2×#100 | D173 | semidirect |
| 184. #100 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012291 | 2 |
| C2×#19149705 | 2 |
| #26012257 | 2 |
| #26011760 | 2 |
| #26011753 | 2 |
| #26011539 | 2 |
| #26011473 | 2 |
| C2×#100×C173 | 2 |
| #3068 | 173 |