Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
390 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26012045 | C2 | semidirect |
| 3. #26011884 | C2 | semidirect |
| 4. #26011852 | C2 | semidirect |
| 5. #26011698 | C2 | semidirect |
| 6. #26011692 | C2 | semidirect |
| 7. #26011691 | C2 | semidirect |
| 8. #26011656 | C2 | semidirect |
| 9. #26011652 | C2 | semidirect |
| 10. #26011547 | C2 | semidirect |
| 11. #462×C173 | C2 | semidirect |
| 140. C173 | #3216 | semidirect |
| 147. #462 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012045 | 2 |
| #26012042 | 2 |
| #26011884 | 2 |
| #26011852 | 2 |
| #26011698 | 2 |
| #26011692 | 2 |
| #26011691 | 2 |
| #26011656 | 2 |
| #26011652 | 2 |
| #26011547 | 2 |
| #462×C173 | 2 |
| #3216 | 173 |