Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 86. Dic89 | Q64 | semidirect |
| 98. C89 | #13688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151438 | 2 |
| #26022503 | 2 |
| Q32×Dic89 | 2 |
| #26018447 | 2 |
| #26018434 | 2 |
| #26018433 | 2 |
| C2×Q64×C89 | 2 |
| #13688 | 89 |