Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
444 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 46. Dic712 | Q8 | semidirect |
| 134. C89 | #33957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033140 | 2 |
| #26022537 | 2 |
| #26022415 | 2 |
| #26022413 | 2 |
| #26022403 | 2 |
| #26022160 | 2 |
| #26022122 | 2 |
| C4×Dic712 | 2 |
| C89×#2253 | 2 |
| #33957 | 89 |