Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1426 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1426 conjugacy classes of subgroups — too many to draw. Only its 259 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 |
|---|---|---|
| 7. C23×Q8×C89 | C4 | semidirect |
| 11. C22×C4⋊C4×C89 | C4 | semidirect |
| 12. C22×C4⋊C4×C89 | C4 | semidirect |
| 18. C2×C22⋊Dic89 | Q8 | semidirect |
| 153. C89 | #11381 | semidirect |
| 154. C23×Q8 | Dic89 | semidirect |
| 158. C22×C4⋊C4 | Dic89 | semidirect |
| 159. C22×C4⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151365 | 2 |
| #26018475 | 2 |
| C22×C22⋊Q8×C89 | 2 |
| #11381 | 89 |