Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
296 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 21. #362×C89 | C4 | semidirect |
| 132. C89 | #13157 | semidirect |
| 144. #362 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151414 | 2 |
| #26021856 | 2 |
| #26021168 | 2 |
| #26021043 | 2 |
| #26018364 | 2 |
| #26018363 | 2 |
| C2×#362×C89 | 2 |
| #13157 | 89 |