Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
452 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26033402 | C2 | semidirect |
| 2. #26033401 | C2 | semidirect |
| 3. #26022572 | C2 | semidirect |
| 4. #26022571 | C2 | semidirect |
| 5. #26022568 | C2 | semidirect |
| 6. #26022560 | C2 | semidirect |
| 7. #26022559 | C2 | semidirect |
| 8. C2×#19151438 | C2 | semidirect |
| 9. Q64×D89 | C2 | semidirect |
| 10. #26022547 | C2 | semidirect |
| 11. C89×#2264 | C2 | semidirect |
| 165. #2264 | D89 | semidirect |
| 171. C89 | #33984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033402 | 2 |
| #26033401 | 2 |
| #26022572 | 2 |
| #26022571 | 2 |
| #26022568 | 2 |
| #26022560 | 2 |
| #26022559 | 2 |
| C2×#19151438 | 2 |
| Q64×D89 | 2 |
| #26022547 | 2 |
| C89×#2264 | 2 |
| #33984 | 89 |