Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
312 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 2. #26021851 | C2 | semidirect |
| 4. #26021043 | C2 | semidirect |
| 5. #26018367 | C2 | semidirect |
| 6. #26018349 | C2 | semidirect |
| 23. #362×C89 | C4 | semidirect |
| 24. #361×C89 | C4 | semidirect |
| 148. C89 | #13146 | semidirect |
| 159. #362 | Dic89 | semidirect |
| 160. #361 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151405 | 2 |
| #26021851 | 2 |
| #26021151 | 2 |
| #26021043 | 2 |
| #26018367 | 2 |
| #26018349 | 2 |
| C89×#2148 | 2 |
| #13146 | 89 |