Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1078 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 251 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×#19151646 | C2 | semidirect |
| 3. #26021651 | C2 | direct (N × H) |
| 4. C2×#338×C89 | C2 | semidirect |
| 8. #19151646 | C22 | semidirect |
| 14. #338×C89 | C22 | semidirect |
| 117. C2×C89 | #2069 | semidirect |
| 123. C2×#338 | D89 | semidirect |
| 124. C89 | C2×#2069 | semidirect |
| 134. #338 | C2×D89 | semidirect |
| 237. C2 | #26021651 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151646 | 2 |
| C22×#15667928 | 2 |
| #26021651 | 2 |
| C2×#338×C89 | 2 |
| C2×#2069 | 89 |