Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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. #26012327 | C2 | semidirect |
| 2. C2×#19149707 | C2 | semidirect |
| 3. #26012055 | C2 | semidirect |
| 4. #26011666 | C2 | semidirect |
| 5. #26011661 | C2 | semidirect |
| 6. #26011507 | C2 | semidirect |
| 7. #413×C173 | C2 | semidirect |
| 8. #19149727 | C22 | semidirect |
| 12. #19149724 | C22 | semidirect |
| 16. C22×D692 | C22 | semidirect |
| 18. #19149707 | C22 | semidirect |
| 21. #19149675 | C22 | semidirect |
| 22. #19149668 | C22 | semidirect |
| 25. #19149638 | C22 | semidirect |
| 26. #19149605 | C22 | semidirect |
| 28. C2×M16×C173 | C22 | semidirect |
| 29. #101×C173 | C22 | semidirect |
| 30. #100×C173 | C22 | semidirect |
| 38. #14583826 | D4 | semidirect |
| 43. C2×Dic346 | D4 | semidirect |
| 49. C2×D692 | D4 | semidirect |
| 134. C173 | #3021 | semidirect |
| 142. #413 | D173 | semidirect |
| 157. C2×M16 | C2×D173 | semidirect |
| 164. #101 | C2×D173 | semidirect |
| 165. #100 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012327 | 2 |
| C2×#19149707 | 2 |
| #26012055 | 2 |
| #26011666 | 2 |
| #26011661 | 2 |
| #26011507 | 2 |
| #413×C173 | 2 |
| #3021 | 173 |