Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012304 | C2 | semidirect |
| 2. #26012300 | C2 | semidirect |
| 3. #26012296 | C2 | semidirect |
| 4. #26011876 | C2 | semidirect |
| 5. #26011762 | C2 | semidirect |
| 6. #26011757 | C2 | semidirect |
| 7. #26011667 | C2 | semidirect |
| 8. #26011666 | C2 | semidirect |
| 9. #26011607 | C2 | semidirect |
| 10. #26011606 | C2 | semidirect |
| 11. #473×C173 | C2 | semidirect |
| 12. #19149727 | C22 | semidirect |
| 16. #19149710 | C22 | semidirect |
| 19. #19149707 | C22 | semidirect |
| 27. C2×#14583813 | C22 | semidirect |
| 31. #19149687 | C22 | semidirect |
| 32. #19149685 | C22 | semidirect |
| 33. #19149668 | C22 | semidirect |
| 34. #19149614 | C22 | semidirect |
| 36. #19149605 | C22 | semidirect |
| 37. #19149605 | C22 | semidirect |
| 38. #19149595 | C22 | semidirect |
| 39. C8×Dic173 | C22 | semidirect |
| 41. C2×Q16×C173 | C22 | semidirect |
| 43. #108×C173 | C22 | semidirect |
| 44. #101×C173 | C22 | semidirect |
| 149. C173 | #3290 | semidirect |
| 155. #473 | D173 | semidirect |
| 178. C2×Q16 | C2×D173 | semidirect |
| 188. #108 | C2×D173 | semidirect |
| 192. #101 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012304 | 2 |
| #26012300 | 2 |
| #26012296 | 2 |
| #26011876 | 2 |
| #26011762 | 2 |
| #26011757 | 2 |
| #26011667 | 2 |
| #26011666 | 2 |
| #26011607 | 2 |
| #26011606 | 2 |
| #473×C173 | 2 |
| #3290 | 173 |