Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1372 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1372 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 |
|---|---|---|
| 1. C2×#19152229 | C2 | semidirect |
| 3. #26019191 | C2 | direct (N × H) |
| 4. C2×#19151334 | C2 | semidirect |
| 5. C2×#19151324 | C2 | semidirect |
| 10. #19152229 | C22 | semidirect |
| 20. #19151334 | C22 | semidirect |
| 21. #19151324 | C22 | semidirect |
| 126. C22×C4×C89 | SD16 | semidirect |
| 181. C2×C4×C89 | C2×SD16 | semidirect |
| 225. C2×C89 | #1599 | semidirect |
| 235. C89 | C2×#1599 | semidirect |
| 341. C22×C4 | #13083562 | semidirect |
| 417. C2×C4 | C2×#13083562 | semidirect |
| 453. C2 | #26019191 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152229 | 2 |
| C2×#19151749 | 2 |
| #26019191 | 2 |
| C2×#19151334 | 2 |
| C2×#19151324 | 2 |
| C2×#394×C89 | 2 |
| C2×#1599 | 89 |