Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26012047 | C2 | semidirect |
| 3. #26011848 | C2 | semidirect |
| 4. #26011846 | C2 | semidirect |
| 5. #26011845 | C2 | semidirect |
| 6. #26011840 | C2 | semidirect |
| 7. #26011836 | C2 | semidirect |
| 8. #26011486 | C2 | semidirect |
| 9. #26011484 | C2 | semidirect |
| 10. C4×C8×D173 | C2 | semidirect |
| 11. #488×C173 | C2 | semidirect |
| 114. C173 | #3131 | semidirect |
| 121. #488 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012047 | 2 |
| #26012040 | 2 |
| #26011848 | 2 |
| #26011846 | 2 |
| #26011845 | 2 |
| #26011840 | 2 |
| #26011836 | 2 |
| #26011486 | 2 |
| #26011484 | 2 |
| C4×C8×D173 | 2 |
| #488×C173 | 2 |
| #3131 | 173 |