Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
584 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19149707 | C2 | semidirect |
| 2. C2×#19149705 | C2 | semidirect |
| 3. C2×#19149675 | C2 | semidirect |
| 4. #26011959 | C2 | semidirect |
| 5. #26011690 | C2 | semidirect |
| 6. #26011685 | C2 | semidirect |
| 7. #26011514 | C2 | semidirect |
| 8. #26011495 | C2 | semidirect |
| 9. #418×C173 | C2 | semidirect |
| 15. C2×#14583815 | C22 | semidirect |
| 16. C2×#14583814 | C22 | semidirect |
| 17. C2×D1384 | C22 | semidirect |
| 18. C2×#14583811 | C22 | semidirect |
| 23. #19149644 | C22 | semidirect |
| 24. #19149641 | C22 | semidirect |
| 29. #19149608 | C22 | semidirect |
| 30. #19149599 | C22 | semidirect |
| 34. #102×C173 | C22 | semidirect |
| 37. #14583826 | D4 | semidirect |
| 79. Dic346 | C2×D4 | semidirect |
| 84. D692 | C2×D4 | semidirect |
| 125. Dic173 | AGL(1,ℤ/8) | semidirect |
| 132. C173 | #3038 | semidirect |
| 142. #418 | D173 | semidirect |
| 167. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| C2×#19149705 | 2 |
| C2×#19149675 | 2 |
| #26011959 | 2 |
| #26011690 | 2 |
| #26011685 | 2 |
| #26011514 | 2 |
| #26011495 | 2 |
| #418×C173 | 2 |
| #3038 | 173 |