Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012305 | C2 | semidirect |
| 2. #26012303 | C2 | semidirect |
| 3. #26012293 | C2 | semidirect |
| 4. #26011875 | C2 | semidirect |
| 5. #26011767 | C2 | semidirect |
| 6. #26011762 | C2 | semidirect |
| 7. #26011754 | C2 | semidirect |
| 8. #26011670 | C2 | semidirect |
| 9. #26011665 | C2 | semidirect |
| 10. #26011609 | C2 | semidirect |
| 11. #443×C173 | C2 | semidirect |
| 12. #19149726 | C22 | semidirect |
| 16. #19149709 | C22 | semidirect |
| 19. #19149707 | C22 | semidirect |
| 26. C2×Dic692 | C22 | semidirect |
| 29. C2×#14583815 | C22 | semidirect |
| 33. #19149685 | C22 | semidirect |
| 34. #19149667 | C22 | semidirect |
| 35. #19149615 | C22 | semidirect |
| 37. #19149607 | C22 | semidirect |
| 38. #19149597 | C22 | semidirect |
| 39. #19149595 | C22 | semidirect |
| 41. #131×C173 | C22 | semidirect |
| 42. #108×C173 | C22 | semidirect |
| 43. #104×C173 | C22 | semidirect |
| 44. C4×C8×C173 | C22 | semidirect |
| 149. C173 | #3290 | semidirect |
| 161. #443 | D173 | semidirect |
| 185. #131 | C2×D173 | semidirect |
| 188. #108 | C2×D173 | semidirect |
| 191. #104 | C2×D173 | semidirect |
| 194. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012305 | 2 |
| #26012303 | 2 |
| #26012293 | 2 |
| #26011875 | 2 |
| #26011767 | 2 |
| #26011762 | 2 |
| #26011754 | 2 |
| #26011670 | 2 |
| #26011665 | 2 |
| #26011609 | 2 |
| #443×C173 | 2 |
| #3290 | 173 |