Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 246 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 |
|---|---|---|
| 2. #26019870 | C2 | semidirect |
| 3. #26018322 | C2 | semidirect |
| 4. #26018300 | C2 | semidirect |
| 72. C8×C89 | SD32 | semidirect |
| 96. C89 | #12426 | semidirect |
| 163. C8 | #15667956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022297 | 2 |
| #26019870 | 2 |
| #26018322 | 2 |
| #26018300 | 2 |
| C8×D8×C89 | 2 |
| #12426 | 89 |