Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 492 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. #26032675 | C2 | semidirect |
| 2. #26022527 | C2 | semidirect |
| 3. #26022444 | C2 | semidirect |
| 4. #26022400 | C2 | semidirect |
| 5. #26022338 | C2 | semidirect |
| 6. C4×D1424 | C2 | semidirect |
| 7. #26022036 | C2 | semidirect |
| 8. D4×C16×C89 | C2 | semidirect |
| 124. D4×C16 | D89 | semidirect |
| 126. C89 | #33908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032675 | 2 |
| #26022527 | 2 |
| #26022444 | 2 |
| #26022400 | 2 |
| #26022338 | 2 |
| C4×D1424 | 2 |
| #26022036 | 2 |
| D4×C16×C89 | 2 |
| #33908 | 89 |