Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149724 | C2 | semidirect |
| 2. C2×#19149707 | C2 | semidirect |
| 3. C22×#14583811 | C2 | semidirect |
| 4. #26012060 | C2 | semidirect |
| 5. #26011637 | C2 | semidirect |
| 6. #26011626 | C2 | semidirect |
| 7. #26011485 | C2 | semidirect |
| 8. #26011459 | C2 | semidirect |
| 9. #418×C173 | C2 | semidirect |
| 15. C2×#14583825 | C22 | semidirect |
| 16. C22×D692 | C22 | semidirect |
| 19. C2×D4×D173 | C22 | semidirect |
| 21. C2×#14583815 | C22 | semidirect |
| 22. C2×D1384 | C22 | semidirect |
| 24. C2×#14583811 | C22 | semidirect |
| 25. C22×#13063436 | C22 | semidirect |
| 28. #19149654 | C22 | semidirect |
| 30. #19149602 | C22 | semidirect |
| 31. #19149599 | C22 | semidirect |
| 32. #19149591 | C22 | semidirect |
| 34. C2×M16×C173 | C22 | semidirect |
| 35. #117×C173 | C22 | semidirect |
| 36. #102×C173 | C22 | semidirect |
| 42. #14583826 | D4 | semidirect |
| 75. C2×D4×C173 | D4 | semidirect |
| 151. C173 | #3008 | semidirect |
| 159. #418 | D173 | semidirect |
| 178. C2×M16 | C2×D173 | semidirect |
| 184. #117 | C2×D173 | semidirect |
| 187. #102 | C2×D173 | semidirect |
| 218. C2×D4 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149724 | 2 |
| C2×#19149707 | 2 |
| C22×#14583811 | 2 |
| #26012060 | 2 |
| #26011637 | 2 |
| #26011626 | 2 |
| #26011485 | 2 |
| #26011459 | 2 |
| #418×C173 | 2 |
| #3008 | 173 |