Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
336 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26022424 | C2 | semidirect |
| 3. #26022423 | C2 | semidirect |
| 4. #26019885 | C2 | semidirect |
| 5. #26018290 | C2 | semidirect |
| 6. #26018229 | C2 | semidirect |
| 7. C89×#1336 | C2 | semidirect |
| 168. #1336 | D89 | semidirect |
| 169. C89 | #12367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032057 | 2 |
| #26022424 | 2 |
| #26022423 | 2 |
| #26019885 | 2 |
| #26018290 | 2 |
| #26018229 | 2 |
| C89×#1336 | 2 |
| #12367 | 89 |