Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
572 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #26028245 | C2 | semidirect |
| 3. #26018379 | C2 | semidirect |
| 4. #26018378 | C2 | semidirect |
| 38. 2−1+4×C89 | Q8 | semidirect |
| 173. C89 | #13378 | semidirect |
| 190. 2−1+4 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028245 | 2 |
| #26020211 | 2 |
| #26018379 | 2 |
| #26018378 | 2 |
| C89×#1793 | 2 |
| #13378 | 89 |