Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
280 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26022067 | C2 | semidirect |
| 3. #26022016 | C2 | semidirect |
| 4. #26018314 | C2 | semidirect |
| 5. #26018312 | C2 | semidirect |
| 6. #26018293 | C2 | semidirect |
| 7. C89×#1359 | C2 | semidirect |
| 146. #1359 | D89 | semidirect |
| 147. C89 | #11991 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030877 | 2 |
| #26022067 | 2 |
| #26022016 | 2 |
| #26018314 | 2 |
| #26018312 | 2 |
| #26018293 | 2 |
| C89×#1359 | 2 |
| #11991 | 89 |