Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
242 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 9. #19151351 | C4 | semidirect |
| 11. C4⋊C16×C89 | C4 | semidirect |
| 97. C89 | #7296 | semidirect |
| 102. C4⋊C16 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667946 | 2 |
| #26019011 | 2 |
| C89×#2162 | 2 |
| #7296 | 89 |