Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022066 | C2 | semidirect |
| 3. #26021855 | C2 | semidirect |
| 4. #26018286 | C2 | semidirect |
| 5. #26018286 | C2 | semidirect |
| 6. #26018285 | C2 | semidirect |
| 7. C89×#1355 | C2 | semidirect |
| 143. #1355 | D89 | semidirect |
| 144. C89 | #11912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030879 | 2 |
| #26022066 | 2 |
| #26021855 | 2 |
| #26018286 | 2 |
| #26018285 | 2 |
| C89×#1355 | 2 |
| #11912 | 89 |