Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 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. #26012027 | C2 | semidirect |
| 2. C2×#19149641 | C2 | semidirect |
| 3. #26011804 | C2 | semidirect |
| 4. #26011790 | C2 | semidirect |
| 5. #26011709 | C2 | semidirect |
| 6. #26011641 | C2 | semidirect |
| 8. #26011602 | C2 | semidirect |
| 9. #26011594 | C2 | semidirect |
| 10. #26011545 | C2 | semidirect |
| 11. #483×C173 | C2 | semidirect |
| 17. #19149670 | C22 | semidirect |
| 18. #19149668 | C22 | semidirect |
| 21. Q8×Dic173 | C22 | semidirect |
| 26. #19149641 | C22 | semidirect |
| 31. #19149612 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 35. #19149599 | C22 | semidirect |
| 37. #19149589 | C22 | semidirect |
| 40. #106×C173 | C22 | semidirect |
| 41. #103×C173 | C22 | semidirect |
| 140. C173 | #3114 | semidirect |
| 144. #483 | D173 | semidirect |
| 175. #106 | C2×D173 | semidirect |
| 177. #103 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012027 | 2 |
| C2×#19149641 | 2 |
| #26011804 | 2 |
| #26011790 | 2 |
| #26011709 | 2 |
| #26011641 | 2 |
| #26011627 | 2 |
| #26011602 | 2 |
| #26011594 | 2 |
| #26011545 | 2 |
| #483×C173 | 2 |
| #3114 | 173 |