Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19149699 | C2 | semidirect |
| 3. #26012055 | C2 | semidirect |
| 4. #26011972 | C2 | semidirect |
| 5. #26011716 | C2 | semidirect |
| 6. #26011709 | C2 | semidirect |
| 7. #26011690 | C2 | semidirect |
| 8. #26011685 | C2 | semidirect |
| 9. #26011519 | C2 | semidirect |
| 10. C2×#19149599 | C2 | semidirect |
| 11. #417×C173 | C2 | semidirect |
| 16. C2×#14583816 | C22 | semidirect |
| 18. C2×#14583814 | C22 | semidirect |
| 19. C2×#14583813 | C22 | semidirect |
| 21. C2×#14583811 | C22 | semidirect |
| 28. #19149644 | C22 | semidirect |
| 29. #19149641 | C22 | semidirect |
| 34. #19149608 | C22 | semidirect |
| 35. #19149608 | C22 | semidirect |
| 41. #103×C173 | C22 | semidirect |
| 42. #102×C173 | C22 | semidirect |
| 45. #14583826 | D4 | semidirect |
| 154. C173 | #3045 | semidirect |
| 165. #417 | D173 | semidirect |
| 194. #103 | C2×D173 | semidirect |
| 197. #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×#19149699 | 2 |
| #26012055 | 2 |
| #26011972 | 2 |
| #26011716 | 2 |
| #26011709 | 2 |
| #26011690 | 2 |
| #26011685 | 2 |
| #26011519 | 2 |
| C2×#19149599 | 2 |
| #417×C173 | 2 |
| #3045 | 173 |