Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 15. C22×Q16×C89 | C4 | semidirect |
| 22. C2×#107×C89 | C4 | semidirect |
| 23. C2×#103×C89 | C4 | semidirect |
| 167. C89 | #9814 | semidirect |
| 168. C22×Q16 | Dic89 | semidirect |
| 176. C2×#107 | Dic89 | semidirect |
| 177. C2×#103 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020290 | 2 |
| C8×C22⋊Dic89 | 2 |
| #26018772 | 2 |
| #26018616 | 2 |
| C2×#467×C89 | 2 |
| #9814 | 89 |