Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
716 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. C2×#19151530 | C2 | semidirect |
| 4. #26020336 | C2 | semidirect |
| 6. C2×#19151323 | C2 | semidirect |
| 7. C89×#1294 | C2 | semidirect |
| 255. #1294 | D89 | semidirect |
| 256. C89 | #9919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151912 | 2 |
| #26025997 | 2 |
| C2×#19151530 | 2 |
| #26020336 | 2 |
| C2×#19151331 | 2 |
| C2×#19151323 | 2 |
| C89×#1294 | 2 |
| #9919 | 89 |