Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1222 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1222 conjugacy classes of subgroups — too many to draw. Only its 147 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. #26020326 | C2 | semidirect |
| 7. C23×Q8×C89 | C4 | semidirect |
| 11. C22×C22⋊C4×C89 | C4 | semidirect |
| 13. C22×C42×C89 | C4 | semidirect |
| 134. C89 | #8544 | semidirect |
| 135. C23×Q8 | Dic89 | semidirect |
| 139. C22×C22⋊C4 | Dic89 | semidirect |
| 141. C22×C42 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020326 | 2 |
| #26020167 | 2 |
| C22×#124×C89 | 2 |
| #8544 | 89 |