Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
670 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 227 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. #26022122 | C2 | direct (N × H) |
| 9. C2×Dic712 | C4 | semidirect |
| 32. Dic712 | C2×C4 | semidirect |
| 97. C2×C89 | #2176 | semidirect |
| 106. C89 | C2×#2176 | semidirect |
| 196. C2 | #26022122 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic712 | 2 |
| C2×#19151692 | 2 |
| #26022122 | 2 |
| C2×#19151401 | 2 |
| C2×#19151373 | 2 |
| C2×#367×C89 | 2 |
| C2×#2176 | 89 |