Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
502 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26029323 | C2 | semidirect |
| 2. #26018914 | C2 | semidirect |
| 3. #26018721 | C2 | semidirect |
| 4. #26018151 | C2 | semidirect |
| 135. C89 | #9007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029323 | 2 |
| #26018914 | 2 |
| #26018721 | 2 |
| #26018151 | 2 |
| C89×#3150 | 2 |
| #9007 | 89 |