Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
236 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26022505 | C2 | semidirect |
| 3. #26018324 | C2 | semidirect |
| 4. #26018302 | C2 | semidirect |
| 56. D4×C89 | Q32 | semidirect |
| 92. C89 | #12431 | semidirect |
| 145. D4 | Dic712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022505 | 2 |
| #26019617 | 2 |
| #26018324 | 2 |
| #26018302 | 2 |
| D4×C16×C89 | 2 |
| #12431 | 89 |