Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
604 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 171 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. #26022466 | C2 | direct (N × H) |
| 3. C2×#19151422 | C2 | semidirect |
| 4. C2×#19151410 | C2 | semidirect |
| 5. C2×#19151380 | C2 | semidirect |
| 6. C2×#430×C89 | C2 | semidirect |
| 14. #19151422 | C22 | semidirect |
| 15. #19151410 | C22 | semidirect |
| 16. #19151380 | C22 | semidirect |
| 20. #430×C89 | C22 | semidirect |
| 150. C2×C89 | #2238 | semidirect |
| 154. C2×#430 | D89 | semidirect |
| 159. C89 | C2×#2238 | semidirect |
| 168. #430 | C2×D89 | semidirect |
| 303. C2 | #26022466 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151851 | 2 |
| #26022466 | 2 |
| C2×#19151422 | 2 |
| C2×#19151410 | 2 |
| C2×#19151380 | 2 |
| C2×#430×C89 | 2 |
| C2×#2238 | 89 |