Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26012258 | C2 | semidirect |
| 3. #26011509 | C2 | semidirect |
| 4. #26011457 | C2 | semidirect |
| 5. #26011261 | C2 | semidirect |
| 6. #26011256 | C2 | semidirect |
| 7. #416×C173 | C2 | semidirect |
| 10. #19149709 | C4 | semidirect |
| 12. #19149704 | C4 | semidirect |
| 118. C173 | #1881 | semidirect |
| 123. #416 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012289 | 2 |
| #26012258 | 2 |
| #26011509 | 2 |
| #26011457 | 2 |
| #26011261 | 2 |
| #26011256 | 2 |
| #416×C173 | 2 |
| #1881 | 173 |