Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 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×#19149698 | C2 | semidirect |
| 2. C2×#19149687 | C2 | semidirect |
| 3. #26012070 | C2 | semidirect |
| 4. #26011750 | C2 | semidirect |
| 5. #26011749 | C2 | semidirect |
| 6. #26011741 | C2 | semidirect |
| 7. #26011719 | C2 | semidirect |
| 8. #26011718 | C2 | semidirect |
| 9. #106×D173 | C2 | semidirect |
| 10. #26011489 | C2 | semidirect |
| 11. #469×C173 | C2 | semidirect |
| 64. C8×D173 | D4 | semidirect |
| 139. C173 | #3060 | semidirect |
| 147. #469 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149698 | 2 |
| C2×#19149687 | 2 |
| #26012070 | 2 |
| #26011750 | 2 |
| #26011749 | 2 |
| #26011741 | 2 |
| #26011719 | 2 |
| #26011718 | 2 |
| #106×D173 | 2 |
| #26011489 | 2 |
| #469×C173 | 2 |
| #3060 | 173 |