Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26022514 | C2 | semidirect |
| 3. #26022133 | C2 | semidirect |
| 4. #26018449 | C2 | semidirect |
| 5. #26018445 | C2 | semidirect |
| 6. #26018443 | C2 | semidirect |
| 7. C89×#2264 | C2 | semidirect |
| 97. #2264 | D89 | semidirect |
| 104. C89 | #13691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022564 | 2 |
| #26022514 | 2 |
| #26022133 | 2 |
| #26018449 | 2 |
| #26018445 | 2 |
| #26018443 | 2 |
| C89×#2264 | 2 |
| #13691 | 89 |