Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 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. #26022533 | C2 | semidirect |
| 3. #26018459 | C2 | semidirect |
| 4. #26018449 | C2 | semidirect |
| 7. C89×#1426 | C2 | semidirect |
| 22. Dic712 | Q8 | semidirect |
| 24. D1424 | Q8 | semidirect |
| 81. #1426 | D89 | semidirect |
| 85. C89 | #13710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022533 | 2 |
| #26022132 | 2 |
| #26018459 | 2 |
| #26018449 | 2 |
| #26018440 | 2 |
| #26018438 | 2 |
| C89×#1426 | 2 |
| #13710 | 89 |