Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
636 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 351 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. #26022024 | C2 | semidirect |
| 4. C2×#19151420 | C2 | semidirect |
| 7. #19152015 | C4 | semidirect |
| 20. #15667952 | C2×C4 | semidirect |
| 22. C2×#13083549 | C2×C4 | semidirect |
| 89. C89 | #33404 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033355 | 2 |
| #26028863 | 2 |
| #26022024 | 2 |
| C2×#19151420 | 2 |
| C89×#2912 | 2 |
| #33404 | 89 |