Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
296 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022491 | C2 | semidirect |
| 3. #26022386 | C2 | semidirect |
| 4. #26018294 | C2 | semidirect |
| 5. #26018234 | C2 | semidirect |
| 6. #26018218 | C2 | semidirect |
| 7. C89×#1696 | C2 | semidirect |
| 150. #1696 | D89 | semidirect |
| 154. C89 | #12388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033342 | 2 |
| #26022491 | 2 |
| #26022386 | 2 |
| #26018294 | 2 |
| #26018234 | 2 |
| #26018218 | 2 |
| C89×#1696 | 2 |
| #12388 | 89 |