Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26012095 | C2 | semidirect |
| 2. #26012059 | C2 | semidirect |
| 3. #26011867 | C2 | semidirect |
| 4. #26011856 | C2 | semidirect |
| 5. #26011845 | C2 | semidirect |
| 6. #26011708 | C2 | semidirect |
| 7. #26011684 | C2 | semidirect |
| 8. #26011635 | C2 | semidirect |
| 9. #26011623 | C2 | semidirect |
| 10. #26011553 | C2 | semidirect |
| 11. #496×C173 | C2 | semidirect |
| 15. C2×#14583811 | C22 | semidirect |
| 18. #19149671 | C22 | semidirect |
| 25. D4×Dic173 | C22 | semidirect |
| 27. #19149608 | C22 | semidirect |
| 28. #19149603 | C22 | semidirect |
| 30. #19149601 | C22 | semidirect |
| 33. C4×#13063436 | C22 | semidirect |
| 34. C2×SD16×C173 | C22 | semidirect |
| 36. #127×C173 | C22 | semidirect |
| 38. #97×C173 | C22 | semidirect |
| 128. C173 | #3220 | semidirect |
| 132. #496 | D173 | semidirect |
| 143. C2×SD16 | C2×D173 | semidirect |
| 149. #127 | C2×D173 | semidirect |
| 166. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012095 | 2 |
| #26012059 | 2 |
| #26011867 | 2 |
| #26011856 | 2 |
| #26011845 | 2 |
| #26011708 | 2 |
| #26011684 | 2 |
| #26011635 | 2 |
| #26011623 | 2 |
| #26011553 | 2 |
| #496×C173 | 2 |
| #3220 | 173 |