Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
670 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 670 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 |
|---|---|---|
| 3. #26018376 | C2 | semidirect |
| 5. C2×#15667971 | C4 | semidirect |
| 6. C22×C4×Dic89 | C4 | semidirect |
| 9. #19151505 | C4 | semidirect |
| 175. C89 | #12857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022743 | 2 |
| #26020170 | 2 |
| #26018376 | 2 |
| C89×#1782 | 2 |
| #12857 | 89 |