Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
810 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26021921 | C2 | semidirect |
| 2. C2×#19151391 | C2 | semidirect |
| 3. #26020360 | C2 | semidirect |
| 15. #535×C89 | C4 | semidirect |
| 17. #533×C89 | C4 | semidirect |
| 20. #518×C89 | C4 | semidirect |
| 22. C4×#41×C89 | C4 | semidirect |
| 185. C89 | #12727 | semidirect |
| 190. #535 | Dic89 | semidirect |
| 192. #533 | Dic89 | semidirect |
| 195. #518 | Dic89 | semidirect |
| 197. C4×#41 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021921 | 2 |
| C2×#19151391 | 2 |
| #26020360 | 2 |
| C89×#3508 | 2 |
| #12727 | 89 |