Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 67. C8×C89 | Q32 | semidirect |
| 88. C89 | #12494 | semidirect |
| 151. C8 | Dic712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022303 | 2 |
| #26019870 | 2 |
| #26019150 | 2 |
| #26018302 | 2 |
| C89×#1367 | 2 |
| #12494 | 89 |