Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 28. C22×Dic178 | Q8 | semidirect |
| 38. C2×C4⋊Dic89 | Q8 | semidirect |
| 218. C89 | #10375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025263 | 2 |
| #26021236 | 2 |
| #26018825 | 2 |
| C2×#19151334 | 2 |
| #26018119 | 2 |
| #26018099 | 2 |
| C89×#1294 | 2 |
| #10375 | 89 |