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×#19149687 | C2 | semidirect |
| 3. #26012057 | C2 | semidirect |
| 4. #26011745 | C2 | semidirect |
| 5. #26011744 | C2 | semidirect |
| 6. #26011741 | C2 | semidirect |
| 7. #26011726 | C2 | semidirect |
| 8. #26011725 | C2 | semidirect |
| 9. #26011526 | C2 | semidirect |
| 10. #26011494 | C2 | semidirect |
| 11. #469×C173 | C2 | semidirect |
| 19. C2×#14583809 | C22 | semidirect |
| 20. C22×#13063436 | C22 | semidirect |
| 22. C2×C8×D173 | C22 | semidirect |
| 25. #19149654 | C22 | semidirect |
| 26. #19149653 | C22 | semidirect |
| 27. #19149650 | C22 | semidirect |
| 31. #19149612 | C22 | semidirect |
| 32. #19149611 | C22 | semidirect |
| 33. #19149601 | C22 | semidirect |
| 34. #19149600 | C22 | semidirect |
| 35. #19149599 | C22 | semidirect |
| 37. C2×M16×C173 | C22 | semidirect |
| 38. #121×C173 | C22 | semidirect |
| 39. #106×C173 | C22 | semidirect |
| 40. #102×C173 | C22 | semidirect |
| 65. C8×D173 | D4 | semidirect |
| 146. C173 | #3058 | semidirect |
| 154. #469 | D173 | semidirect |
| 168. C2×M16 | C2×D173 | semidirect |
| 177. #121 | C2×D173 | semidirect |
| 183. #106 | C2×D173 | semidirect |
| 187. #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×#19149687 | 2 |
| #26012057 | 2 |
| #26011745 | 2 |
| #26011744 | 2 |
| #26011741 | 2 |
| #26011726 | 2 |
| #26011725 | 2 |
| #26011526 | 2 |
| #26011494 | 2 |
| #469×C173 | 2 |
| #3058 | 173 |