Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
546 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 167 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. #26028863 | C2 | semidirect |
| 3. #26022472 | C2 | semidirect |
| 4. #26022467 | C2 | semidirect |
| 5. C2×#19151421 | C2 | semidirect |
| 6. #26022002 | C2 | semidirect |
| 7. C89×#2115 | C2 | semidirect |
| 151. #2115 | D89 | semidirect |
| 152. C89 | #33659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029914 | 2 |
| #26028863 | 2 |
| #26022472 | 2 |
| #26022467 | 2 |
| C2×#19151421 | 2 |
| #26022002 | 2 |
| C89×#2115 | 2 |
| #33659 | 89 |