Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1154 conjugacy classes of subgroups; only the 391 normal subgroups are shown.
This group has 1154 conjugacy classes of subgroups — too many to draw. Only its 391 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 |
|---|---|---|
| 1. #26033355 | C2 | semidirect |
| 2. #26028863 | C2 | semidirect |
| 3. #26022001 | C2 | semidirect |
| 4. C2×#19151411 | C2 | semidirect |
| 8. C2×#15667952 | C22 | semidirect |
| 10. C2×#15667948 | C22 | semidirect |
| 11. #19151414 | C22 | semidirect |
| 12. #19151411 | C22 | semidirect |
| 121. C89 | #33392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033355 | 2 |
| #26028863 | 2 |
| #26022001 | 2 |
| C2×#19151411 | 2 |
| C2×#576×C89 | 2 |
| #33392 | 89 |