Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26012039 | C2 | semidirect |
| 2. #124×D173 | C2 | semidirect |
| 3. #26011878 | C2 | semidirect |
| 4. #26011851 | C2 | semidirect |
| 5. #26011850 | C2 | semidirect |
| 6. #26011708 | C2 | semidirect |
| 7. #26011704 | C2 | semidirect |
| 8. #26011628 | C2 | semidirect |
| 9. #26011623 | C2 | semidirect |
| 10. #26011546 | C2 | semidirect |
| 11. #496×C173 | C2 | semidirect |
| 15. C2×#14583814 | C22 | semidirect |
| 17. #19149679 | C22 | semidirect |
| 27. D4×Dic173 | C22 | semidirect |
| 31. #19149608 | C22 | semidirect |
| 32. #19149604 | C22 | semidirect |
| 33. #19149603 | C22 | semidirect |
| 37. #19149590 | C22 | semidirect |
| 38. C2×SD16×C173 | C22 | semidirect |
| 40. #127×C173 | C22 | semidirect |
| 42. #97×C173 | C22 | semidirect |
| 150. C173 | #3213 | semidirect |
| 155. #496 | D173 | semidirect |
| 167. C2×SD16 | C2×D173 | semidirect |
| 171. #127 | C2×D173 | semidirect |
| 193. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012039 | 2 |
| #124×D173 | 2 |
| #26011878 | 2 |
| #26011851 | 2 |
| #26011850 | 2 |
| #26011708 | 2 |
| #26011704 | 2 |
| #26011628 | 2 |
| #26011623 | 2 |
| #26011546 | 2 |
| #496×C173 | 2 |
| #3213 | 173 |