Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1020 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26026368 | C2 | semidirect |
| 3. C2×#19151336 | C2 | semidirect |
| 4. C2×#19151335 | C2 | semidirect |
| 6. #26018094 | C2 | semidirect |
| 95. C22×Dic89 | SD16 | semidirect |
| 274. C89 | #9966 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151749 | 2 |
| #26026368 | 2 |
| C2×#19151336 | 2 |
| C2×#19151335 | 2 |
| #26018493 | 2 |
| #26018094 | 2 |
| C2×#450×C89 | 2 |
| #9966 | 89 |