Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D173 | C2 | semidirect |
| 2. C2×#19149685 | C2 | semidirect |
| 3. #26012057 | C2 | semidirect |
| 4. #26011743 | C2 | semidirect |
| 5. #26011742 | C2 | semidirect |
| 6. #26011728 | C2 | semidirect |
| 7. #26011727 | C2 | semidirect |
| 8. #26011724 | C2 | semidirect |
| 9. #26011528 | C2 | semidirect |
| 10. #26011494 | C2 | semidirect |
| 11. #466×C173 | C2 | semidirect |
| 18. C2×#14583810 | C22 | semidirect |
| 20. C2×#14583809 | C22 | semidirect |
| 22. C2×C8×D173 | C22 | semidirect |
| 25. #19149654 | C22 | semidirect |
| 26. #19149653 | C22 | semidirect |
| 27. #19149650 | C22 | semidirect |
| 31. #19149613 | C22 | semidirect |
| 32. #19149610 | C22 | semidirect |
| 33. #19149601 | C22 | semidirect |
| 34. #19149600 | C22 | semidirect |
| 35. #19149599 | C22 | semidirect |
| 37. C22×C8×C173 | C22 | semidirect |
| 38. #121×C173 | C22 | semidirect |
| 39. #107×C173 | C22 | semidirect |
| 40. #102×C173 | C22 | semidirect |
| 65. C8×D173 | D4 | semidirect |
| 150. C173 | #3058 | semidirect |
| 160. #466 | D173 | semidirect |
| 175. C22×C8 | C2×D173 | semidirect |
| 181. #121 | C2×D173 | semidirect |
| 186. #107 | C2×D173 | semidirect |
| 191. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D173 | 2 |
| C2×#19149685 | 2 |
| #26012057 | 2 |
| #26011743 | 2 |
| #26011742 | 2 |
| #26011728 | 2 |
| #26011727 | 2 |
| #26011724 | 2 |
| #26011528 | 2 |
| #26011494 | 2 |
| #466×C173 | 2 |
| #3058 | 173 |