Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1938 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1938 conjugacy classes of subgroups — too many to draw. Only its 291 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. C2×#19152398 | C2 | semidirect |
| 2. C2×#19151566 | C2 | semidirect |
| 3. #26021357 | C2 | direct (N × H) |
| 4. C2×#338×C89 | C2 | semidirect |
| 8. #19152398 | C22 | semidirect |
| 14. #19151566 | C22 | semidirect |
| 17. #338×C89 | C22 | semidirect |
| 145. C2×C89 | #2017 | semidirect |
| 151. C2×#338 | D89 | semidirect |
| 152. C89 | C2×#2017 | semidirect |
| 165. #338 | C2×D89 | semidirect |
| 293. C2 | #26021357 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152398 | 2 |
| C2×#19151566 | 2 |
| #26021357 | 2 |
| C2×#338×C89 | 2 |
| C2×#2017 | 89 |