Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 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. #26012305 | C2 | semidirect |
| 2. #26012304 | C2 | semidirect |
| 3. #26011934 | C2 | semidirect |
| 4. #26011933 | C2 | semidirect |
| 5. #26011930 | C2 | semidirect |
| 6. #26011922 | C2 | semidirect |
| 7. #26011921 | C2 | semidirect |
| 8. C2×#19149625 | C2 | semidirect |
| 9. Q32×D173 | C2 | semidirect |
| 10. #26011909 | C2 | semidirect |
| 11. #510×C173 | C2 | semidirect |
| 123. C173 | #3417 | semidirect |
| 130. #510 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012305 | 2 |
| #26012304 | 2 |
| #26011934 | 2 |
| #26011933 | 2 |
| #26011930 | 2 |
| #26011922 | 2 |
| #26011921 | 2 |
| C2×#19149625 | 2 |
| Q32×D173 | 2 |
| #26011909 | 2 |
| #510×C173 | 2 |
| #3417 | 173 |