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×#19149701 | C2 | semidirect |
| 3. #26012060 | C2 | semidirect |
| 4. #26011971 | C2 | semidirect |
| 5. #26011714 | C2 | semidirect |
| 6. #26011707 | C2 | semidirect |
| 7. #26011692 | C2 | semidirect |
| 8. #26011687 | C2 | semidirect |
| 9. #26011493 | C2 | semidirect |
| 10. C2×#19149601 | C2 | semidirect |
| 11. #424×C173 | C2 | semidirect |
| 17. C2×Dic692 | C22 | semidirect |
| 19. C2×#14583815 | C22 | semidirect |
| 20. C2×#14583815 | C22 | semidirect |
| 22. C2×D1384 | C22 | semidirect |
| 28. C4×Dic346 | C22 | semidirect |
| 29. C4×D692 | C22 | semidirect |
| 34. #19149604 | C22 | semidirect |
| 37. #19149601 | C22 | semidirect |
| 41. C4⋊C8×C173 | C22 | semidirect |
| 42. C4⋊C8×C173 | C22 | semidirect |
| 47. #14583826 | D4 | semidirect |
| 154. C173 | #3045 | semidirect |
| 164. #424 | D173 | semidirect |
| 192. C4⋊C8 | C2×D173 | semidirect |
| 193. C4⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| C2×#19149701 | 2 |
| #26012060 | 2 |
| #26011971 | 2 |
| #26011714 | 2 |
| #26011707 | 2 |
| #26011692 | 2 |
| #26011687 | 2 |
| #26011493 | 2 |
| C2×#19149601 | 2 |
| #424×C173 | 2 |
| #3045 | 173 |