Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
336 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #26022519 | C2 | semidirect |
| 2. #26022287 | C2 | semidirect |
| 3. #26019736 | C2 | semidirect |
| 4. #26018295 | C2 | semidirect |
| 5. #26018234 | C2 | semidirect |
| 6. #26018219 | C2 | semidirect |
| 7. C89×#3403 | C2 | semidirect |
| 162. #3403 | D89 | semidirect |
| 169. C89 | #12336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022519 | 2 |
| #26022287 | 2 |
| #26019736 | 2 |
| #26018295 | 2 |
| #26018234 | 2 |
| #26018219 | 2 |
| C89×#3403 | 2 |
| #12336 | 89 |