Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19149700 | C2 | semidirect |
| 3. #26012042 | C2 | semidirect |
| 4. #26012040 | C2 | semidirect |
| 5. #26011884 | C2 | semidirect |
| 6. #26011883 | C2 | semidirect |
| 7. #26011881 | C2 | semidirect |
| 8. #26011880 | C2 | semidirect |
| 9. #26011877 | C2 | semidirect |
| 10. #97×D173 | C2 | semidirect |
| 11. #497×C173 | C2 | semidirect |
| 65. C8×D173 | D4 | semidirect |
| 133. C173 | #3150 | semidirect |
| 141. #497 | 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×#19149700 | 2 |
| #26012042 | 2 |
| #26012040 | 2 |
| #26011884 | 2 |
| #26011883 | 2 |
| #26011881 | 2 |
| #26011880 | 2 |
| #26011877 | 2 |
| #97×D173 | 2 |
| #497×C173 | 2 |
| #3150 | 173 |