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×#19149702 | C2 | semidirect |
| 2. C2×#19149687 | C2 | semidirect |
| 3. #26012071 | C2 | semidirect |
| 4. #26011746 | C2 | semidirect |
| 5. #26011745 | C2 | semidirect |
| 6. #26011744 | C2 | semidirect |
| 7. #26011723 | C2 | semidirect |
| 8. #26011722 | C2 | semidirect |
| 9. #106×D173 | C2 | semidirect |
| 10. #26011491 | C2 | semidirect |
| 11. #470×C173 | C2 | semidirect |
| 65. C8×D173 | D4 | semidirect |
| 139. C173 | #3060 | semidirect |
| 145. #470 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149702 | 2 |
| C2×#19149687 | 2 |
| #26012071 | 2 |
| #26011746 | 2 |
| #26011745 | 2 |
| #26011744 | 2 |
| #26011723 | 2 |
| #26011722 | 2 |
| #106×D173 | 2 |
| #26011491 | 2 |
| #470×C173 | 2 |
| #3060 | 173 |