Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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. C22×#14583811 | C2 | semidirect |
| 2. C2×#19149686 | C2 | semidirect |
| 3. #26012055 | C2 | semidirect |
| 4. #26011742 | C2 | semidirect |
| 5. #26011725 | C2 | semidirect |
| 6. #26011527 | C2 | semidirect |
| 7. #26011496 | C2 | semidirect |
| 8. #26011495 | C2 | semidirect |
| 9. #535×C173 | C2 | semidirect |
| 16. C2×#14583810 | C22 | semidirect |
| 18. C22×#13063436 | C22 | semidirect |
| 21. #19149653 | C22 | semidirect |
| 24. #19149612 | C22 | semidirect |
| 25. #19149610 | C22 | semidirect |
| 26. #19149600 | C22 | semidirect |
| 27. #19149599 | C22 | semidirect |
| 32. #121×C173 | C22 | semidirect |
| 46. C2×#13063436 | D4 | semidirect |
| 125. C173 | #3058 | semidirect |
| 130. #535 | D173 | semidirect |
| 152. #121 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| C2×#19149686 | 2 |
| #26012055 | 2 |
| #26011742 | 2 |
| #26011725 | 2 |
| #26011527 | 2 |
| #26011496 | 2 |
| #26011495 | 2 |
| #535×C173 | 2 |
| #3058 | 173 |