Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
702 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 195 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 |
|---|---|---|
| 3. #26022340 | C2 | direct (N × H) |
| 4. C2×#19151424 | C2 | semidirect |
| 5. C2×#19151402 | C2 | semidirect |
| 6. C22×Q32×C89 | C2 | semidirect |
| 16. #19151424 | C22 | semidirect |
| 17. #19151402 | C22 | semidirect |
| 20. C2×Q32×C89 | C22 | semidirect |
| 82. C22×D89 | Q32 | semidirect |
| 111. C2×D89 | C2×Q32 | semidirect |
| 119. C2×C89 | #2216 | semidirect |
| 124. C22×Q32 | D89 | semidirect |
| 130. C89 | C2×#2216 | semidirect |
| 135. C2×Q32 | C2×D89 | semidirect |
| 243. C2 | #26022340 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D89 | 2 |
| C2×#19151836 | 2 |
| #26022340 | 2 |
| C2×#19151424 | 2 |
| C2×#19151402 | 2 |
| C22×Q32×C89 | 2 |
| C2×#2216 | 89 |