Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
686 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 686 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 |
|---|---|---|
| 1. #26023010 | C2 | semidirect |
| 4. #26018785 | C2 | semidirect |
| 5. #26018161 | C2 | semidirect |
| 6. #26018106 | C2 | semidirect |
| 27. #451×C89 | C4 | semidirect |
| 28. #450×C89 | C4 | semidirect |
| 274. C89 | #9524 | semidirect |
| 279. #451 | Dic89 | semidirect |
| 280. #450 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023010 | 2 |
| #26020196 | 2 |
| #26020170 | 2 |
| #26018785 | 2 |
| #26018161 | 2 |
| #26018106 | 2 |
| C89×#3007 | 2 |
| #9524 | 89 |