Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
390 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #26022047 | C2 | semidirect |
| 3. #26022001 | C2 | semidirect |
| 4. #26021872 | C2 | semidirect |
| 5. #26020312 | C2 | semidirect |
| 6. #26018350 | C2 | semidirect |
| 7. C2×#360×C89 | C2 | semidirect |
| 180. C2×#360 | D89 | semidirect |
| 184. C89 | #13391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029968 | 2 |
| #26022047 | 2 |
| #26022001 | 2 |
| #26021872 | 2 |
| #26020312 | 2 |
| #26018350 | 2 |
| C2×#360×C89 | 2 |
| #13391 | 89 |