Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
308 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 24. C2×#13083549 | Q8 | semidirect |
| 107. C89 | #13269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022018 | 2 |
| #26021857 | 2 |
| #26018338 | 2 |
| #26018332 | 2 |
| C89×#2961 | 2 |
| #13269 | 89 |