Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
506 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 165 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. #26033258 | C2 | semidirect |
| 3. #26022480 | C2 | semidirect |
| 4. #26022395 | C2 | semidirect |
| 7. Q8×C16×C89 | C2 | semidirect |
| 72. Q8×C89 | SD32 | semidirect |
| 109. Q8×C16 | D89 | semidirect |
| 111. C89 | #33926 | semidirect |
| 179. Q8 | #15667957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033258 | 2 |
| Q8×D712 | 2 |
| #26022480 | 2 |
| #26022395 | 2 |
| #26022298 | 2 |
| C4×#15667957 | 2 |
| Q8×C16×C89 | 2 |
| #33926 | 89 |