Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
3246 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 3246 conjugacy classes of subgroups — too many to draw. Only its 491 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. #26018501 | C2 | semidirect |
| 3. #26018475 | C2 | semidirect |
| 8. C2×#15667919 | C22 | semidirect |
| 12. C22×C22⋊C4×C89 | C4 | semidirect |
| 116. C89 | #14341 | semidirect |
| 122. C22×C22⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151454 | 2 |
| #26018501 | 2 |
| #26018475 | 2 |
| C23×C22⋊C4×C89 | 2 |
| #14341 | 89 |