Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1264 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1264 conjugacy classes of subgroups — too many to draw. Only its 203 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. C2×#19151917 | C2 | semidirect |
| 3. C2×#19151537 | C2 | semidirect |
| 4. #26019291 | C2 | direct (N × H) |
| 5. C2×#19151333 | C2 | semidirect |
| 6. C2×#324×C89 | C2 | semidirect |
| 17. #19151917 | C22 | semidirect |
| 21. #19151537 | C22 | semidirect |
| 25. #19151333 | C22 | semidirect |
| 28. #324×C89 | C22 | semidirect |
| 204. C2×C89 | #1616 | semidirect |
| 214. C2×#324 | D89 | semidirect |
| 215. C89 | C2×#1616 | semidirect |
| 237. #324 | C2×D89 | semidirect |
| 413. C2 | #26019291 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152179 | 2 |
| C2×#19151917 | 2 |
| C2×#19151537 | 2 |
| #26019291 | 2 |
| C2×#19151333 | 2 |
| C2×#324×C89 | 2 |
| C2×#1616 | 89 |