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. #26012287 | C2 | semidirect |
| 2. C2×#19149698 | C2 | semidirect |
| 3. #131×D173 | C2 | semidirect |
| 4. #26011767 | C2 | semidirect |
| 5. #26011766 | C2 | semidirect |
| 6. #26011758 | C2 | semidirect |
| 7. #26011753 | C2 | semidirect |
| 8. #26011752 | C2 | semidirect |
| 9. #108×D173 | C2 | semidirect |
| 10. #26011472 | C2 | semidirect |
| 11. #472×C173 | C2 | semidirect |
| 25. C2×Dic692 | C22 | semidirect |
| 26. C2×#14583814 | C22 | semidirect |
| 37. #19149615 | C22 | semidirect |
| 38. #19149614 | C22 | semidirect |
| 39. #19149597 | C22 | semidirect |
| 40. #19149597 | C22 | semidirect |
| 41. #19149596 | C22 | semidirect |
| 43. C2×D8×C173 | C22 | semidirect |
| 45. #108×C173 | C22 | semidirect |
| 46. #100×C173 | C22 | semidirect |
| 166. C173 | #3067 | semidirect |
| 174. #472 | D173 | semidirect |
| 195. C2×D8 | C2×D173 | semidirect |
| 209. #108 | C2×D173 | semidirect |
| 213. #100 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012287 | 2 |
| C2×#19149698 | 2 |
| #131×D173 | 2 |
| #26011767 | 2 |
| #26011766 | 2 |
| #26011758 | 2 |
| #26011753 | 2 |
| #26011752 | 2 |
| #108×D173 | 2 |
| #26011472 | 2 |
| #472×C173 | 2 |
| #3067 | 173 |