Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1214 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 187 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. #26030183 | C2 | semidirect |
| 3. #26021469 | C2 | semidirect |
| 4. #26020700 | C2 | semidirect |
| 5. #26020466 | C2 | semidirect |
| 6. #26020210 | C2 | semidirect |
| 7. #26020176 | C2 | semidirect |
| 8. C89×#2310 | C2 | semidirect |
| 207. #2310 | D89 | semidirect |
| 213. C89 | #24023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033903 | 2 |
| #26030183 | 2 |
| #26021469 | 2 |
| #26020700 | 2 |
| #26020466 | 2 |
| #26020210 | 2 |
| #26020176 | 2 |
| C89×#2310 | 2 |
| #24023 | 89 |