Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
864 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26020544 | C2 | semidirect |
| 3. #26018570 | C2 | semidirect |
| 4. #26018568 | C2 | semidirect |
| 5. C89×#1869 | C2 | semidirect |
| 277. #1869 | D89 | semidirect |
| 280. C89 | #8317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033661 | 2 |
| #26020544 | 2 |
| #26018570 | 2 |
| #26018568 | 2 |
| C89×#1869 | 2 |
| #8317 | 89 |