Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 2. #26018910 | C2 | semidirect |
| 4. #26018750 | C2 | semidirect |
| 6. #26018083 | C2 | semidirect |
| 7. C89×#1940 | C2 | semidirect |
| 190. #1940 | D89 | semidirect |
| 196. C89 | #10547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030598 | 2 |
| #26018910 | 2 |
| #26018902 | 2 |
| #26018750 | 2 |
| #26018746 | 2 |
| #26018083 | 2 |
| C89×#1940 | 2 |
| #10547 | 89 |