Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
540 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 49. #15667929 | Q8 | semidirect |
| 51. #15667927 | Q8 | semidirect |
| 67. #99×C89 | Q8 | semidirect |
| 232. C89 | #13461 | semidirect |
| 289. #99 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026625 | 2 |
| #26020533 | 2 |
| #26020462 | 2 |
| #26018376 | 2 |
| #26018370 | 2 |
| #26018369 | 2 |
| C89×#1867 | 2 |
| #13461 | 89 |