Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 8. C22×#13083564 | C4 | semidirect |
| 16. C2×#15667945 | C4 | semidirect |
| 17. C2×#15667936 | C4 | semidirect |
| 18. C2×#15667935 | C4 | semidirect |
| 214. C89 | #9814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151837 | 2 |
| #26020288 | 2 |
| #26020026 | 2 |
| #26018773 | 2 |
| #26018772 | 2 |
| #26018615 | 2 |
| C89×#1472 | 2 |
| #9814 | 89 |