Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 3. #26018138 | C2 | semidirect |
| 4. #26018104 | C2 | semidirect |
| 16. #382×C89 | C4 | semidirect |
| 17. #381×C89 | C4 | semidirect |
| 20. C4×C4⋊C4×C89 | C4 | semidirect |
| 21. C4×C22⋊C4×C89 | C4 | semidirect |
| 178. C89 | #8778 | semidirect |
| 185. #382 | Dic89 | semidirect |
| 186. #381 | Dic89 | semidirect |
| 189. C4×C4⋊C4 | Dic89 | semidirect |
| 191. C4×C22⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667927 | 2 |
| #26018590 | 2 |
| #26018138 | 2 |
| #26018104 | 2 |
| C89×#2357 | 2 |
| #8778 | 89 |