Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
180 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 53 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×Dic1424 | C2 | semidirect |
| 4. #26018444 | C2 | semidirect |
| 5. C89×#1425 | C2 | semidirect |
| 70. #1425 | D89 | semidirect |
| 72. C89 | #13701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic1424 | 2 |
| #26022545 | 2 |
| #26022378 | 2 |
| #26018444 | 2 |
| C89×#1425 | 2 |
| #13701 | 89 |