Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #26020405 | C2 | semidirect |
| 3. #26019037 | C2 | semidirect |
| 6. #26018146 | C2 | semidirect |
| 7. C89×#1283 | C2 | semidirect |
| 186. #1283 | D89 | semidirect |
| 187. C89 | #8876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029388 | 2 |
| #26020405 | 2 |
| #26019037 | 2 |
| #26018739 | 2 |
| #26018666 | 2 |
| #26018146 | 2 |
| C89×#1283 | 2 |
| #8876 | 89 |