Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1182 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 139 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×#19151391 | C2 | semidirect |
| 2. #26020170 | C2 | semidirect |
| 5. C2×#15667927 | C22 | semidirect |
| 9. C23×D4×C89 | C4 | semidirect |
| 12. C2×#124×C89 | C4 | semidirect |
| 15. C2×#117×C89 | C4 | semidirect |
| 163. C89 | #12697 | semidirect |
| 165. C23×D4 | Dic89 | semidirect |
| 168. C2×#124 | Dic89 | semidirect |
| 171. C2×#117 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| #26020170 | 2 |
| C2×#535×C89 | 2 |
| #12697 | 89 |