Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
484 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 48. #15667927 | Q8 | semidirect |
| 64. #100×C89 | Q8 | semidirect |
| 66. #99×C89 | Q8 | semidirect |
| 226. C89 | #13463 | semidirect |
| 273. #100 | Dic178 | semidirect |
| 277. #99 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028195 | 2 |
| #26020535 | 2 |
| #26020532 | 2 |
| #26020464 | 2 |
| #26018376 | 2 |
| #26018371 | 2 |
| C89×#1390 | 2 |
| #13463 | 89 |