Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#19151356 | C2 | semidirect |
| 3. #26018247 | C2 | semidirect |
| 4. #26018244 | C2 | semidirect |
| 5. C2×#349×C89 | C2 | semidirect |
| 192. C2×#349 | D89 | semidirect |
| 196. C89 | #11688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029861 | 2 |
| C2×#19151356 | 2 |
| #26018247 | 2 |
| #26018244 | 2 |
| C2×#349×C89 | 2 |
| #11688 | 89 |