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×#19149725 | C2 | semidirect |
| 2. C2×#19149704 | C2 | semidirect |
| 3. C22×D1384 | C2 | semidirect |
| 4. #26012060 | C2 | semidirect |
| 5. #26011639 | C2 | semidirect |
| 6. #26011626 | C2 | semidirect |
| 7. #26011495 | C2 | semidirect |
| 8. #26011457 | C2 | semidirect |
| 9. #416×C173 | C2 | semidirect |
| 12. C2×#14583827 | C22 | semidirect |
| 17. C22×D692 | C22 | semidirect |
| 19. C2×D4×D173 | C22 | semidirect |
| 21. C2×#14583813 | C22 | semidirect |
| 23. C2×D1384 | C22 | semidirect |
| 24. C2×#14583811 | C22 | semidirect |
| 25. C2×#14583810 | C22 | semidirect |
| 28. #19149654 | C22 | semidirect |
| 30. #19149599 | C22 | semidirect |
| 31. #19149591 | C22 | semidirect |
| 33. C22×C8×C173 | C22 | semidirect |
| 34. #117×C173 | C22 | semidirect |
| 35. #103×C173 | C22 | semidirect |
| 36. #102×C173 | C22 | semidirect |
| 55. C2×D692 | D4 | semidirect |
| 72. #41×C173 | D4 | semidirect |
| 151. C173 | #3008 | semidirect |
| 160. #416 | D173 | semidirect |
| 179. C22×C8 | C2×D173 | semidirect |
| 184. #117 | C2×D173 | semidirect |
| 185. #103 | C2×D173 | semidirect |
| 187. #102 | C2×D173 | semidirect |
| 198. #41 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149725 | 2 |
| C2×#19149704 | 2 |
| C22×D1384 | 2 |
| #26012060 | 2 |
| #26011639 | 2 |
| #26011626 | 2 |
| #26011495 | 2 |
| #26011457 | 2 |
| #416×C173 | 2 |
| #3008 | 173 |