Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 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×#19149698 | C2 | semidirect |
| 2. C22×C8×D173 | C2 | semidirect |
| 3. #26012001 | C2 | semidirect |
| 4. #26011733 | C2 | semidirect |
| 5. #26011732 | C2 | semidirect |
| 6. #26011724 | C2 | semidirect |
| 7. #26011719 | C2 | semidirect |
| 8. #26011718 | C2 | semidirect |
| 9. #26011528 | C2 | semidirect |
| 10. #26011484 | C2 | semidirect |
| 11. #466×C173 | C2 | semidirect |
| 15. C2×Dic692 | C22 | semidirect |
| 16. C2×#14583814 | C22 | semidirect |
| 31. #19149613 | C22 | semidirect |
| 32. #19149610 | C22 | semidirect |
| 33. #19149604 | C22 | semidirect |
| 34. #19149602 | C22 | semidirect |
| 35. #19149600 | C22 | semidirect |
| 36. C2×D8×C173 | C22 | semidirect |
| 39. #107×C173 | C22 | semidirect |
| 40. #102×C173 | C22 | semidirect |
| 63. C8×D173 | D4 | semidirect |
| 121. C22×C173 | #135 | semidirect |
| 129. C2×D173 | #135 | semidirect |
| 145. C173 | #3050 | semidirect |
| 153. #466 | D173 | semidirect |
| 163. C2×D8 | C2×D173 | semidirect |
| 181. #107 | C2×D173 | semidirect |
| 186. #102 | C2×D173 | semidirect |
| 274. C22 | #19149698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149698 | 2 |
| C22×C8×D173 | 2 |
| #26012001 | 2 |
| #26011733 | 2 |
| #26011732 | 2 |
| #26011724 | 2 |
| #26011719 | 2 |
| #26011718 | 2 |
| #26011528 | 2 |
| #26011484 | 2 |
| #466×C173 | 2 |
| #3050 | 173 |