Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 476 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. #26033117 | C2 | semidirect |
| 2. #26022529 | C2 | semidirect |
| 3. #26022527 | C2 | semidirect |
| 4. #26022407 | C2 | semidirect |
| 5. #26022399 | C2 | semidirect |
| 6. C16×Dic178 | C2 | semidirect |
| 45. D16×C89 | Q8 | semidirect |
| 118. C89 | #33947 | semidirect |
| 147. D16 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033117 | 2 |
| #26022529 | 2 |
| #26022527 | 2 |
| #26022407 | 2 |
| #26022399 | 2 |
| C16×Dic178 | 2 |
| D16×Dic89 | 2 |
| C4×D16×C89 | 2 |
| #33947 | 89 |