Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1098 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#19151393 | C2 | semidirect |
| 2. C2×#19151391 | C2 | semidirect |
| 3. #26020170 | C2 | semidirect |
| 10. C22×#41×C89 | C4 | semidirect |
| 14. C2×C4⋊Q8×C89 | C4 | semidirect |
| 16. C2×#124×C89 | C4 | semidirect |
| 20. C22×C42×C89 | C4 | semidirect |
| 207. C89 | #12695 | semidirect |
| 208. C22×#41 | Dic89 | semidirect |
| 212. C2×C4⋊Q8 | Dic89 | semidirect |
| 214. C2×#124 | Dic89 | semidirect |
| 218. C22×C42 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151393 | 2 |
| C2×#19151391 | 2 |
| #26020170 | 2 |
| C2×#532×C89 | 2 |
| #12695 | 89 |