Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. C2×#19151404 | C2 | semidirect |
| 3. C2×#19151373 | C2 | semidirect |
| 4. #26021138 | C2 | semidirect |
| 5. C2×#368×C89 | C2 | semidirect |
| 9. C2×Dic712 | C4 | semidirect |
| 10. C2×#15667957 | C4 | semidirect |
| 11. C2×D1424 | C4 | semidirect |
| 126. C2×#368 | D89 | semidirect |
| 130. C89 | #13242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152030 | 2 |
| C2×#19151404 | 2 |
| C2×#19151373 | 2 |
| #26021138 | 2 |
| C2×#368×C89 | 2 |
| #13242 | 89 |