Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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. #26022396 | C2 | semidirect |
| 3. C8×D712 | C2 | semidirect |
| 4. #26018316 | C2 | semidirect |
| 5. #26018310 | C2 | semidirect |
| 6. #26018298 | C2 | semidirect |
| 7. C89×#1706 | C2 | semidirect |
| 48. D712 | SD16 | semidirect |
| 117. #1706 | D89 | semidirect |
| 122. C89 | #12418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022396 | 2 |
| #26022284 | 2 |
| C8×D712 | 2 |
| #26018316 | 2 |
| #26018310 | 2 |
| #26018298 | 2 |
| C89×#1706 | 2 |
| #12418 | 89 |