Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1770 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 451 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. C2×#19151466 | C2 | semidirect |
| 2. C2×C42×Dic89 | C2 | semidirect |
| 4. #26018484 | C2 | semidirect |
| 14. C2×#126×C89 | C4 | semidirect |
| 61. C42×C89 | C22⋊C4 | semidirect |
| 85. C2×Dic89 | #126 | semidirect |
| 111. C89 | #14711 | semidirect |
| 114. C2×#126 | Dic89 | semidirect |
| 167. C42 | C22⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151466 | 2 |
| C2×C42×Dic89 | 2 |
| #26018489 | 2 |
| #26018484 | 2 |
| C22×#126×C89 | 2 |
| #14711 | 89 |