Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
262 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 82. C8×C89 | Q32 | semidirect |
| 105. C89 | #12504 | semidirect |
| 180. C8 | #15667958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022525 | 2 |
| #26022504 | 2 |
| #26022481 | 2 |
| #26022479 | 2 |
| #26019849 | 2 |
| C8×#13083549 | 2 |
| C89×#1707 | 2 |
| #12504 | 89 |