Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
960 conjugacy classes of subgroups; only the 247 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 247 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. #26021654 | C2 | semidirect |
| 4. #26021651 | C2 | semidirect |
| 5. C2×#338×C89 | C2 | semidirect |
| 130. C2×#338 | D89 | semidirect |
| 131. C89 | #23622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151646 | 2 |
| C2×#19151580 | 2 |
| #26021654 | 2 |
| #26021651 | 2 |
| C2×#338×C89 | 2 |
| #23622 | 89 |