Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
748 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 748 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 |
|---|---|---|
| 2. #26021085 | C2 | semidirect |
| 3. #26018983 | C2 | semidirect |
| 4. #26018975 | C2 | semidirect |
| 5. #26018765 | C2 | semidirect |
| 6. #26018761 | C2 | semidirect |
| 7. C89×#1536 | C2 | semidirect |
| 9. #19152309 | C4 | semidirect |
| 12. #19152268 | C4 | semidirect |
| 226. #1536 | D89 | semidirect |
| 229. C89 | #8493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034650 | 2 |
| #26021085 | 2 |
| #26018983 | 2 |
| #26018975 | 2 |
| #26018765 | 2 |
| #26018761 | 2 |
| C89×#1536 | 2 |
| #8493 | 89 |