Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 147 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. #26033119 | C2 | semidirect |
| 2. #26022536 | C2 | semidirect |
| 3. #26022531 | C2 | semidirect |
| 4. #26022409 | C2 | semidirect |
| 5. #26022407 | C2 | semidirect |
| 6. #26022387 | C2 | semidirect |
| 7. #26022160 | C2 | semidirect |
| 58. D16×C89 | Q8 | semidirect |
| 140. C89 | #33956 | semidirect |
| 178. D16 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033119 | 2 |
| #26022536 | 2 |
| #26022531 | 2 |
| #26022409 | 2 |
| #26022407 | 2 |
| #26022387 | 2 |
| #26022160 | 2 |
| #26022128 | 2 |
| C4×D16×C89 | 2 |
| #33956 | 89 |