Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1810 conjugacy classes of subgroups; only the 319 normal subgroups are shown.
This group has 1810 conjugacy classes of subgroups — too many to draw. Only its 319 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. #26018514 | C2 | semidirect |
| 2. #26018501 | C2 | semidirect |
| 3. #26018493 | C2 | semidirect |
| 4. #26018489 | C2 | semidirect |
| 15. #392×C89 | C4 | semidirect |
| 160. C89 | #14651 | semidirect |
| 167. #392 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018514 | 2 |
| #26018501 | 2 |
| #26018493 | 2 |
| #26018489 | 2 |
| C2×#392×C89 | 2 |
| #14651 | 89 |