Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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. Q64×D89 | C2 | semidirect |
| 3. #26018469 | C2 | semidirect |
| 4. #26018468 | C2 | semidirect |
| 5. #26018466 | C2 | semidirect |
| 6. #26018462 | C2 | semidirect |
| 7. C89×Q128 | C2 | semidirect |
| 66. Q128 | D89 | semidirect |
| 70. C89 | #13743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022562 | 2 |
| Q64×D89 | 2 |
| #26018469 | 2 |
| #26018468 | 2 |
| #26018466 | 2 |
| #26018462 | 2 |
| C89×Q128 | 2 |
| #13743 | 89 |