Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
256 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 256 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. #26022389 | C2 | semidirect |
| 3. #26019844 | C2 | semidirect |
| 4. #26018316 | C2 | semidirect |
| 5. #26018308 | C2 | semidirect |
| 6. #26018297 | C2 | semidirect |
| 7. C8×D8×C89 | C2 | semidirect |
| 61. D8×C89 | SD16 | semidirect |
| 94. C8×C89 | D16 | semidirect |
| 120. C8×D8 | D89 | semidirect |
| 124. C89 | #12416 | semidirect |
| 174. D8 | #13083563 | semidirect |
| 211. C8 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022389 | 2 |
| #26022287 | 2 |
| #26019844 | 2 |
| #26018316 | 2 |
| #26018308 | 2 |
| #26018297 | 2 |
| C8×D8×C89 | 2 |
| #12416 | 89 |