Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
756 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 143 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×#19151444 | C2 | semidirect |
| 2. #26020320 | C2 | semidirect |
| 4. #26018130 | C2 | semidirect |
| 16. #390×C89 | C4 | semidirect |
| 17. #389×C89 | C4 | semidirect |
| 174. C89 | #9149 | semidirect |
| 180. #390 | Dic89 | semidirect |
| 181. #389 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151444 | 2 |
| #26020320 | 2 |
| C2×#19151332 | 2 |
| #26018130 | 2 |
| C89×#2854 | 2 |
| #9149 | 89 |