Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26012290 | C2 | semidirect |
| 2. C2×#19149702 | C2 | semidirect |
| 3. #131×D173 | C2 | semidirect |
| 4. #26011763 | C2 | semidirect |
| 5. #26011762 | C2 | semidirect |
| 6. #26011761 | C2 | semidirect |
| 7. #26011757 | C2 | semidirect |
| 8. #26011756 | C2 | semidirect |
| 9. #108×D173 | C2 | semidirect |
| 10. #26011474 | C2 | semidirect |
| 11. #473×C173 | C2 | semidirect |
| 25. C2×#14583813 | C22 | semidirect |
| 26. C2×D1384 | C22 | semidirect |
| 37. #19149615 | C22 | semidirect |
| 38. #19149614 | C22 | semidirect |
| 39. #19149598 | C22 | semidirect |
| 40. #19149595 | C22 | semidirect |
| 41. #19149595 | C22 | semidirect |
| 43. C2×Q16×C173 | C22 | semidirect |
| 45. #108×C173 | C22 | semidirect |
| 46. #101×C173 | C22 | semidirect |
| 166. C173 | #3067 | semidirect |
| 172. #473 | D173 | semidirect |
| 193. C2×Q16 | C2×D173 | semidirect |
| 209. #108 | C2×D173 | semidirect |
| 211. #101 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012290 | 2 |
| C2×#19149702 | 2 |
| #131×D173 | 2 |
| #26011763 | 2 |
| #26011762 | 2 |
| #26011761 | 2 |
| #26011757 | 2 |
| #26011756 | 2 |
| #108×D173 | 2 |
| #26011474 | 2 |
| #473×C173 | 2 |
| #3067 | 173 |