Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 17. #19151346 | C4 | semidirect |
| 18. #19151343 | C4 | semidirect |
| 146. C89 | #9579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021228 | 2 |
| C4⋊C8×Dic89 | 2 |
| #26019024 | 2 |
| #26018910 | 2 |
| #26018656 | 2 |
| #26018084 | 2 |
| C89×#1301 | 2 |
| #9579 | 89 |