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. #26033401 | C2 | semidirect |
| 2. #26022571 | C2 | semidirect |
| 3. #26022570 | C2 | semidirect |
| 4. #26022562 | C2 | semidirect |
| 5. #26022561 | C2 | semidirect |
| 6. Q64×D89 | C2 | semidirect |
| 7. #26022545 | C2 | semidirect |
| 8. C2×Q64×C89 | C2 | semidirect |
| 110. C2×Q64 | D89 | semidirect |
| 112. C89 | #33984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033401 | 2 |
| #26022571 | 2 |
| #26022570 | 2 |
| #26022562 | 2 |
| #26022561 | 2 |
| Q64×D89 | 2 |
| #26022545 | 2 |
| C2×Q64×C89 | 2 |
| #33984 | 89 |