Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
274 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 17. #368×C89 | C4 | semidirect |
| 101. C89 | #13171 | semidirect |
| 108. #368 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151424 | 2 |
| #26021848 | 2 |
| #26021038 | 2 |
| #26018362 | 2 |
| C2×#368×C89 | 2 |
| #13171 | 89 |