Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #125×D173 | C2 | semidirect |
| 3. #26011861 | C2 | semidirect |
| 4. #26011860 | C2 | semidirect |
| 5. #26011855 | C2 | semidirect |
| 6. #26011844 | C2 | semidirect |
| 7. #26011489 | C2 | semidirect |
| 8. #26011443 | C2 | semidirect |
| 9. #490×C173 | C2 | semidirect |
| 90. C173 | #3142 | semidirect |
| 97. #490 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012039 | 2 |
| #125×D173 | 2 |
| #26011861 | 2 |
| #26011860 | 2 |
| #26011855 | 2 |
| #26011844 | 2 |
| #26011489 | 2 |
| #26011443 | 2 |
| #490×C173 | 2 |
| #3142 | 173 |