Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19149707 | C2 | semidirect |
| 2. C2×#19149687 | C2 | semidirect |
| 3. #26012072 | C2 | semidirect |
| 4. #26012060 | C2 | semidirect |
| 5. #26011745 | C2 | semidirect |
| 6. #26011738 | C2 | semidirect |
| 7. #26011728 | C2 | semidirect |
| 8. #26011721 | C2 | semidirect |
| 9. #26011485 | C2 | semidirect |
| 10. C2×#19149599 | C2 | semidirect |
| 11. #428×C173 | C2 | semidirect |
| 19. C2×#14583809 | C22 | semidirect |
| 21. C2×C8×D173 | C22 | semidirect |
| 25. #19149659 | C22 | semidirect |
| 29. #19149654 | C22 | semidirect |
| 32. #19149602 | C22 | semidirect |
| 33. #19149602 | C22 | semidirect |
| 36. #19149599 | C22 | semidirect |
| 37. #19149599 | C22 | semidirect |
| 41. #107×C173 | C22 | semidirect |
| 42. #106×C173 | C22 | semidirect |
| 77. M16×C173 | D4 | semidirect |
| 151. C173 | #3062 | semidirect |
| 161. #428 | D173 | semidirect |
| 187. #107 | C2×D173 | semidirect |
| 188. #106 | C2×D173 | semidirect |
| 220. M16 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| C2×#19149687 | 2 |
| #26012072 | 2 |
| #26012060 | 2 |
| #26011745 | 2 |
| #26011738 | 2 |
| #26011728 | 2 |
| #26011721 | 2 |
| #26011485 | 2 |
| C2×#19149599 | 2 |
| #428×C173 | 2 |
| #3062 | 173 |