Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
434 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26012040 | C2 | semidirect |
| 2. #26012039 | C2 | semidirect |
| 3. #26011878 | C2 | semidirect |
| 4. #26011851 | C2 | semidirect |
| 5. #26011850 | C2 | semidirect |
| 6. #26011694 | C2 | semidirect |
| 7. #26011684 | C2 | semidirect |
| 8. #26011635 | C2 | semidirect |
| 9. #26011633 | C2 | semidirect |
| 10. #26011546 | C2 | semidirect |
| 11. #496×C173 | C2 | semidirect |
| 149. C173 | #3214 | semidirect |
| 154. #496 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012040 | 2 |
| #26012039 | 2 |
| #26011878 | 2 |
| #26011851 | 2 |
| #26011850 | 2 |
| #26011694 | 2 |
| #26011684 | 2 |
| #26011635 | 2 |
| #26011633 | 2 |
| #26011546 | 2 |
| #496×C173 | 2 |
| #3214 | 173 |