Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 151 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. #26033241 | C2 | semidirect |
| 3. #26022505 | C2 | semidirect |
| 4. #26022315 | C2 | semidirect |
| 5. #26022298 | C2 | semidirect |
| 6. C4×Dic712 | C2 | semidirect |
| 8. Q8×C16×C89 | C2 | semidirect |
| 122. Q8×C16 | D89 | semidirect |
| 125. C89 | #33960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033241 | 2 |
| #26022513 | 2 |
| #26022505 | 2 |
| #26022315 | 2 |
| #26022298 | 2 |
| C4×Dic712 | 2 |
| C4×D1424 | 2 |
| Q8×C16×C89 | 2 |
| #33960 | 89 |