Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26012036 | C2 | semidirect |
| 2. C2×#19149666 | C2 | semidirect |
| 3. #26011879 | C2 | semidirect |
| 4. #26011849 | C2 | semidirect |
| 5. #26011705 | C2 | semidirect |
| 6. #26011704 | C2 | semidirect |
| 7. #26011632 | C2 | semidirect |
| 8. #26011629 | C2 | semidirect |
| 9. #26011625 | C2 | semidirect |
| 10. #26011545 | C2 | semidirect |
| 11. #447×C173 | C2 | semidirect |
| 14. C2×#14583815 | C22 | semidirect |
| 15. C2×#14583814 | C22 | semidirect |
| 17. #19149678 | C22 | semidirect |
| 18. #19149675 | C22 | semidirect |
| 26. D4×Dic173 | C22 | semidirect |
| 27. #19149641 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 33. #19149604 | C22 | semidirect |
| 34. #19149602 | C22 | semidirect |
| 37. #19149589 | C22 | semidirect |
| 152. C173 | #3213 | semidirect |
| 163. #447 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012036 | 2 |
| C2×#19149666 | 2 |
| #26011879 | 2 |
| #26011849 | 2 |
| #26011705 | 2 |
| #26011704 | 2 |
| #26011632 | 2 |
| #26011629 | 2 |
| #26011625 | 2 |
| #26011545 | 2 |
| #447×C173 | 2 |
| #3213 | 173 |