Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
356 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 356 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 |
|---|---|---|
| 2. #26019028 | C2 | semidirect |
| 3. #26019024 | C2 | semidirect |
| 6. #26018083 | C2 | semidirect |
| 7. C89×#1838 | C2 | semidirect |
| 135. #1838 | D89 | semidirect |
| 141. C89 | #10659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021050 | 2 |
| #26019028 | 2 |
| #26019024 | 2 |
| #26018676 | 2 |
| #26018083 | 2 |
| C89×#1838 | 2 |
| #10659 | 89 |