Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
826 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 219 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. C22×#15667958 | C2 | semidirect |
| 4. #26022521 | C2 | direct (N × H) |
| 5. C2×#19151374 | C2 | semidirect |
| 6. C2×#494×C89 | C2 | semidirect |
| 12. C2×#15667958 | C22 | semidirect |
| 18. #19151374 | C22 | semidirect |
| 23. #494×C89 | C22 | semidirect |
| 132. C2×C89 | #2251 | semidirect |
| 139. C2×#494 | D89 | semidirect |
| 142. C89 | C2×#2251 | semidirect |
| 158. #494 | C2×D89 | semidirect |
| 268. C2 | #26022521 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667958 | 2 |
| C22×#15667955 | 2 |
| C2×#19151982 | 2 |
| #26022521 | 2 |
| C2×#19151374 | 2 |
| C2×#494×C89 | 2 |
| C2×#2251 | 89 |