Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26022529 | C2 | semidirect |
| 3. #26018454 | C2 | semidirect |
| 4. #26018451 | C2 | semidirect |
| 5. #26018447 | C2 | semidirect |
| 86. C89 | #13707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022529 | 2 |
| D16×Dic89 | 2 |
| #26018454 | 2 |
| #26018451 | 2 |
| #26018447 | 2 |
| #26018430 | 2 |
| C89×#1415 | 2 |
| #13707 | 89 |