Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
106 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 41 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. #26011923 | C2 | semidirect |
| 2. #26011331 | C2 | semidirect |
| 3. #26011329 | C2 | semidirect |
| 4. #26011328 | C2 | semidirect |
| 5. #26011326 | C2 | semidirect |
| 6. C2×#19149585 | C2 | semidirect |
| 7. #508×C173 | C2 | semidirect |
| 52. C173 | #2262 | semidirect |
| 55. #508 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011923 | 2 |
| #26011331 | 2 |
| #26011329 | 2 |
| #26011328 | 2 |
| #26011326 | 2 |
| C2×#19149585 | 2 |
| #508×C173 | 2 |
| #2262 | 173 |