Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
532 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26033266 | C2 | semidirect |
| 2. #26022510 | C2 | semidirect |
| 3. #26022305 | C2 | semidirect |
| 4. #26022289 | C2 | semidirect |
| 5. C16×Dic178 | C2 | semidirect |
| 6. C4×Dic712 | C2 | semidirect |
| 7. D16×Dic89 | C2 | semidirect |
| 127. C89 | #33963 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033266 | 2 |
| #26022510 | 2 |
| #26022305 | 2 |
| #26022289 | 2 |
| C16×Dic178 | 2 |
| C4×Dic712 | 2 |
| D16×Dic89 | 2 |
| C89×#2246 | 2 |
| #33963 | 89 |