Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
216 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 51 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. #26022567 | C2 | semidirect |
| 2. #26022565 | C2 | semidirect |
| 3. #26022500 | C2 | semidirect |
| 4. #26022132 | C2 | semidirect |
| 5. #26018449 | C2 | semidirect |
| 6. #26018441 | C2 | semidirect |
| 7. C89×#1419 | C2 | semidirect |
| 28. Dic712 | D4 | semidirect |
| 32. D1424 | D4 | semidirect |
| 106. #1419 | D89 | semidirect |
| 107. C89 | #13692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022567 | 2 |
| #26022565 | 2 |
| #26022500 | 2 |
| #26022132 | 2 |
| #26018449 | 2 |
| #26018441 | 2 |
| C89×#1419 | 2 |
| #13692 | 89 |