Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
338 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 107 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. #19151346 | C4 | semidirect |
| 16. #19151343 | C4 | semidirect |
| 146. C89 | #9580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021229 | 2 |
| #26019026 | 2 |
| #26018910 | 2 |
| #26018654 | 2 |
| #26018149 | 2 |
| #26018085 | 2 |
| C4×C4⋊C8×C89 | 2 |
| #9580 | 89 |