Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26011509 | C2 | semidirect |
| 3. #26011508 | C2 | semidirect |
| 4. #26011488 | C2 | semidirect |
| 5. #26011464 | C2 | semidirect |
| 6. #26011457 | C2 | semidirect |
| 7. #416×C173 | C2 | semidirect |
| 10. #19149726 | C4 | semidirect |
| 12. #19149725 | C4 | semidirect |
| 20. C2×#14583810 | C22 | semidirect |
| 21. #19149638 | C22 | semidirect |
| 29. C22×C8×C173 | C22 | semidirect |
| 30. #117×C173 | C22 | semidirect |
| 166. C173 | #1794 | semidirect |
| 172. #416 | D173 | semidirect |
| 189. C22×C8 | C2×D173 | semidirect |
| 191. #117 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012327 | 2 |
| #26011509 | 2 |
| #26011508 | 2 |
| #26011488 | 2 |
| #26011464 | 2 |
| #26011457 | 2 |
| #416×C173 | 2 |
| #1794 | 173 |