Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
488 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 13. C22×C4⋊C4×C89 | C4 | semidirect |
| 20. #385×C89 | C4 | semidirect |
| 21. #385×C89 | C4 | semidirect |
| 22. #380×C89 | C4 | semidirect |
| 195. C89 | #13297 | semidirect |
| 197. C22×C4⋊C4 | Dic89 | semidirect |
| 207. #385 | Dic89 | semidirect |
| 208. #385 | Dic89 | semidirect |
| 209. #380 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020244 | 2 |
| C4×#15667927 | 2 |
| #26018370 | 2 |
| C89×#2579 | 2 |
| #13297 | 89 |