Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #26012289 | C2 | semidirect |
| 2. C2×#19149705 | C2 | semidirect |
| 3. #26012258 | C2 | semidirect |
| 4. #26011759 | C2 | semidirect |
| 5. #26011752 | C2 | semidirect |
| 6. #26011539 | C2 | semidirect |
| 7. #26011473 | C2 | semidirect |
| 8. C2×#19149596 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C173 | C2 | semidirect |
| 12. #19149709 | C22 | semidirect |
| 16. #19149704 | C22 | semidirect |
| 18. C2×#14583814 | C22 | semidirect |
| 19. C2×#14583811 | C22 | semidirect |
| 21. #19149686 | C22 | semidirect |
| 26. #19149614 | C22 | semidirect |
| 27. #19149597 | C22 | semidirect |
| 28. #19149596 | C22 | semidirect |
| 29. #19149595 | C22 | semidirect |
| 147. C173 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012289 | 2 |
| C2×#19149705 | 2 |
| #26012258 | 2 |
| #26011759 | 2 |
| #26011752 | 2 |
| #26011539 | 2 |
| #26011473 | 2 |
| C2×#19149596 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #3068 | 173 |