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×#19149698 | C2 | semidirect |
| 2. C2×#19149685 | C2 | semidirect |
| 3. #26012070 | C2 | semidirect |
| 4. #26011736 | C2 | semidirect |
| 5. #26011735 | C2 | semidirect |
| 6. #26011733 | C2 | semidirect |
| 7. #26011732 | C2 | semidirect |
| 8. #26011724 | C2 | semidirect |
| 9. #107×D173 | C2 | semidirect |
| 10. #26011489 | C2 | semidirect |
| 11. #466×C173 | C2 | semidirect |
| 64. C8×D173 | D4 | semidirect |
| 143. C173 | #3061 | semidirect |
| 153. #466 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149698 | 2 |
| C2×#19149685 | 2 |
| #26012070 | 2 |
| #26011736 | 2 |
| #26011735 | 2 |
| #26011733 | 2 |
| #26011732 | 2 |
| #26011724 | 2 |
| #107×D173 | 2 |
| #26011489 | 2 |
| #466×C173 | 2 |
| #3061 | 173 |