Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 123 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×#19149701 | C2 | semidirect |
| 2. C2×#19149698 | C2 | semidirect |
| 3. #26012159 | C2 | semidirect |
| 4. #26011866 | C2 | semidirect |
| 5. #26011728 | C2 | semidirect |
| 6. #26011690 | C2 | semidirect |
| 7. #26011637 | C2 | semidirect |
| 8. #26011634 | C2 | semidirect |
| 9. #26011585 | C2 | semidirect |
| 10. C8×C22⋊D173 | C2 | semidirect |
| 11. #466×C173 | C2 | semidirect |
| 56. Dic692 | D4 | semidirect |
| 134. Dic173 | #135 | semidirect |
| 142. C173 | #3287 | semidirect |
| 149. #466 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| C2×#19149698 | 2 |
| #26012159 | 2 |
| #26011866 | 2 |
| #26011728 | 2 |
| #26011690 | 2 |
| #26011637 | 2 |
| #26011634 | 2 |
| #26011585 | 2 |
| C8×C22⋊D173 | 2 |
| #466×C173 | 2 |
| #3287 | 173 |