Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
624 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 624 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 |
|---|---|---|
| 1. C2×#19151388 | C2 | semidirect |
| 3. #26020240 | C2 | semidirect |
| 4. C4×#15667929 | C2 | semidirect |
| 17. C22×C22⋊C4×C89 | C4 | semidirect |
| 22. #381×C89 | C4 | semidirect |
| 23. #380×C89 | C4 | semidirect |
| 24. #379×C89 | C4 | semidirect |
| 233. C89 | #13219 | semidirect |
| 237. C22×C22⋊C4 | Dic89 | semidirect |
| 245. #381 | Dic89 | semidirect |
| 247. #380 | Dic89 | semidirect |
| 248. #379 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151388 | 2 |
| C2×#19151385 | 2 |
| #26020240 | 2 |
| C4×#15667929 | 2 |
| C89×#2534 | 2 |
| #13219 | 89 |