Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. #26022025 | C2 | semidirect |
| 4. #26018367 | C2 | semidirect |
| 17. #349×C89 | C4 | semidirect |
| 42. M32×C89 | C2×C4 | semidirect |
| 126. C89 | #12932 | semidirect |
| 137. #349 | Dic89 | semidirect |
| 156. M32 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028842 | 2 |
| #26022025 | 2 |
| #26020294 | 2 |
| #26018367 | 2 |
| C2×#349×C89 | 2 |
| #12932 | 89 |