Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19149709 | C2 | semidirect |
| 2. C2×#19149686 | C2 | semidirect |
| 3. #26012062 | C2 | semidirect |
| 4. #26011747 | C2 | semidirect |
| 5. #26011735 | C2 | semidirect |
| 6. #26011730 | C2 | semidirect |
| 7. #26011718 | C2 | semidirect |
| 8. #26011531 | C2 | semidirect |
| 9. #26011487 | C2 | semidirect |
| 10. C2×#19149602 | C2 | semidirect |
| 51. #14583810 | D4 | semidirect |
| 143. C173 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149709 | 2 |
| C2×#19149686 | 2 |
| #26012062 | 2 |
| #26011747 | 2 |
| #26011735 | 2 |
| #26011730 | 2 |
| #26011718 | 2 |
| #26011531 | 2 |
| #26011487 | 2 |
| C2×#19149602 | 2 |
| #537×C173 | 2 |
| #3063 | 173 |