Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
956 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 956 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 |
|---|---|---|
| 2. #26020326 | C2 | semidirect |
| 4. #26018156 | C2 | semidirect |
| 14. C2×#123×C89 | C4 | semidirect |
| 17. #386×C89 | C4 | semidirect |
| 39. C23×C4×C89 | C2×C4 | semidirect |
| 40. C23×C4×C89 | C2×C4 | semidirect |
| 52. C2×C22⋊C4×C89 | C2×C4 | semidirect |
| 216. C89 | #9499 | semidirect |
| 218. C2×#123 | Dic89 | semidirect |
| 224. #386 | Dic89 | semidirect |
| 240. C23×C4 | C2×Dic89 | semidirect |
| 241. C23×C4 | C2×Dic89 | semidirect |
| 261. C2×C22⋊C4 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022830 | 2 |
| #26020326 | 2 |
| #26020167 | 2 |
| #26018156 | 2 |
| C89×#2405 | 2 |
| #9499 | 89 |