Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #26021973 | C2 | semidirect |
| 4. #26021167 | C2 | semidirect |
| 6. #26018367 | C2 | semidirect |
| 7. C89×#2153 | C2 | semidirect |
| 164. #2153 | D89 | semidirect |
| 170. C89 | #13443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152041 | 2 |
| #26022002 | 2 |
| #26021973 | 2 |
| #26021167 | 2 |
| #26021150 | 2 |
| #26018367 | 2 |
| C89×#2153 | 2 |
| #13443 | 89 |