Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1800 conjugacy classes of subgroups; only the 1089 normal subgroups are shown.
This group has 1800 conjugacy classes of subgroups — too many to draw. Only its 1089 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 |
|---|---|---|
| 21. #564×C89 | C4 | semidirect |
| 90. C89 | #34526 | semidirect |
| 91. #564 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023438 | 2 |
| #26023352 | 2 |
| #26023058 | 2 |
| #125×Dic89 | 2 |
| C2×#564×C89 | 2 |
| #34526 | 89 |