Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
854 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 854 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. C22×#15667955 | C2 | semidirect |
| 3. C2×#19151983 | C2 | semidirect |
| 4. #26022514 | C2 | direct (N × H) |
| 5. C2×C16×Dic89 | C2 | semidirect |
| 6. C22×Q32×C89 | C2 | semidirect |
| 11. C2×#15667955 | C22 | semidirect |
| 16. #19151983 | C22 | semidirect |
| 18. C16×Dic89 | C22 | semidirect |
| 21. C2×Q32×C89 | C22 | semidirect |
| 114. C2×C89 | #2249 | semidirect |
| 118. C22×Q32 | D89 | semidirect |
| 124. C89 | C2×#2249 | semidirect |
| 130. C2×Q32 | C2×D89 | semidirect |
| 232. C2 | #26022514 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667955 | 2 |
| C22×D1424 | 2 |
| C2×#19151983 | 2 |
| #26022514 | 2 |
| C2×C16×Dic89 | 2 |
| C22×Q32×C89 | 2 |
| C2×#2249 | 89 |