Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26012046 | C2 | semidirect |
| 3. #26011790 | C2 | semidirect |
| 4. #26011789 | C2 | semidirect |
| 5. #26011778 | C2 | semidirect |
| 6. #26011772 | C2 | semidirect |
| 7. #26011771 | C2 | semidirect |
| 8. #26011530 | C2 | semidirect |
| 9. #26011513 | C2 | semidirect |
| 11. #476×C173 | C2 | semidirect |
| 15. #19149679 | C22 | semidirect |
| 16. #19149670 | C22 | semidirect |
| 30. #19149613 | C22 | semidirect |
| 31. #19149612 | C22 | semidirect |
| 32. #19149610 | C22 | semidirect |
| 33. C4⋊#13063436 | C22 | semidirect |
| 34. #19149608 | C22 | semidirect |
| 38. C4⋊Q8×C173 | C22 | semidirect |
| 40. #106×C173 | C22 | semidirect |
| 41. C4⋊C8×C173 | C22 | semidirect |
| 48. D4×D173 | Q8 | semidirect |
| 144. C173 | #3077 | semidirect |
| 151. #476 | D173 | semidirect |
| 161. C4⋊Q8 | C2×D173 | semidirect |
| 180. #106 | C2×D173 | semidirect |
| 183. C4⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| C4×D4×D173 | 2 |
| #26011790 | 2 |
| #26011789 | 2 |
| #26011778 | 2 |
| #26011772 | 2 |
| #26011771 | 2 |
| #26011530 | 2 |
| #26011513 | 2 |
| #26011494 | 2 |
| #476×C173 | 2 |
| #3077 | 173 |