Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
218 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 41. Q16×C89 | Q16 | semidirect |
| 86. C89 | #12448 | semidirect |
| 119. Q16 | Dic356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022404 | 2 |
| #26019870 | 2 |
| #26018322 | 2 |
| #26018311 | 2 |
| C8×Q16×C89 | 2 |
| #12448 | 89 |