Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
370 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 72. C22×Dic89 | Q16 | semidirect |
| 186. C89 | #12219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028514 | 2 |
| #26021418 | 2 |
| #26019209 | 2 |
| #26018276 | 2 |
| #26018274 | 2 |
| #26018181 | 2 |
| C89×#1614 | 2 |
| #12219 | 89 |