Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26020267 | C2 | semidirect |
| 3. #26019023 | C2 | semidirect |
| 6. #26018111 | C2 | semidirect |
| 7. C89×#1461 | C2 | semidirect |
| 187. #1461 | D89 | semidirect |
| 189. C89 | #10467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029724 | 2 |
| #26020267 | 2 |
| #26019023 | 2 |
| #26018899 | 2 |
| #26018813 | 2 |
| #26018111 | 2 |
| C89×#1461 | 2 |
| #10467 | 89 |