Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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×#19149712 | C2 | semidirect |
| 3. #26012062 | C2 | semidirect |
| 4. #26011972 | C2 | semidirect |
| 5. #26011712 | C2 | semidirect |
| 6. #26011705 | C2 | semidirect |
| 7. #26011700 | C2 | semidirect |
| 8. #26011695 | C2 | semidirect |
| 9. #26011519 | C2 | semidirect |
| 10. C2×#19149602 | C2 | semidirect |
| 11. #417×C173 | C2 | semidirect |
| 146. C173 | #3046 | semidirect |
| 157. #417 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149712 | 2 |
| C2×#19149699 | 2 |
| #26012062 | 2 |
| #26011972 | 2 |
| #26011712 | 2 |
| #26011705 | 2 |
| #26011700 | 2 |
| #26011695 | 2 |
| #26011519 | 2 |
| C2×#19149602 | 2 |
| #417×C173 | 2 |
| #3046 | 173 |