Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
414 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26022025 | C2 | semidirect |
| 2. #26021980 | C2 | semidirect |
| 3. #26021968 | C2 | semidirect |
| 4. #26021856 | C2 | semidirect |
| 5. #26021163 | C2 | semidirect |
| 6. #26021151 | C2 | semidirect |
| 24. C2×SD32×C89 | C4 | semidirect |
| 25. C2×D16×C89 | C4 | semidirect |
| 175. C89 | #13247 | semidirect |
| 180. C2×SD32 | Dic89 | semidirect |
| 181. C2×D16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022025 | 2 |
| #26021980 | 2 |
| #26021968 | 2 |
| #26021856 | 2 |
| #26021163 | 2 |
| #26021151 | 2 |
| C2×#509×C89 | 2 |
| #13247 | 89 |