Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26030784 | C2 | semidirect |
| 5. #26018357 | C2 | semidirect |
| 6. #26018339 | C2 | semidirect |
| 7. C89×#1384 | C2 | semidirect |
| 30. C2×Dic356 | Q8 | semidirect |
| 32. C2×D712 | Q8 | semidirect |
| 162. #1384 | D89 | semidirect |
| 164. C89 | #13374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030784 | 2 |
| #26021987 | 2 |
| C2×#19151409 | 2 |
| #26021148 | 2 |
| #26018357 | 2 |
| #26018339 | 2 |
| C89×#1384 | 2 |
| #13374 | 89 |