Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
218 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 84. C8×C89 | Q32 | semidirect |
| 109. C89 | #12421 | semidirect |
| 187. C8 | Dic712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022405 | 2 |
| #26022303 | 2 |
| #26019849 | 2 |
| C8×Dic356 | 2 |
| #26018309 | 2 |
| #26018302 | 2 |
| C89×#1367 | 2 |
| #12421 | 89 |