Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
468 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26029330 | C2 | semidirect |
| 3. #26018972 | C2 | semidirect |
| 4. #26018676 | C2 | semidirect |
| 5. #26018592 | C2 | semidirect |
| 6. #26018115 | C2 | semidirect |
| 7. C89×#1307 | C2 | semidirect |
| 185. #1307 | D89 | semidirect |
| 187. C89 | #9529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030344 | 2 |
| #26029330 | 2 |
| #26018972 | 2 |
| #26018676 | 2 |
| #26018592 | 2 |
| #26018115 | 2 |
| C89×#1307 | 2 |
| #9529 | 89 |