Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26012221 | C2 | semidirect |
| 5. #26011774 | C2 | semidirect |
| 7. #26011698 | C2 | semidirect |
| 8. #26011621 | C2 | semidirect |
| 9. #26011595 | C2 | semidirect |
| 11. #487×C173 | C2 | semidirect |
| 116. C173 | #3369 | semidirect |
| 121. #487 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012221 | 2 |
| #26012215 | 2 |
| #26011852 | 2 |
| #26011778 | 2 |
| #26011774 | 2 |
| #26011716 | 2 |
| #26011698 | 2 |
| #26011621 | 2 |
| #26011595 | 2 |
| C4×#14583815 | 2 |
| #487×C173 | 2 |
| #3369 | 173 |