Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26029104 | C2 | semidirect |
| 2. C2×#19151411 | C2 | semidirect |
| 3. #26021968 | C2 | semidirect |
| 4. #26021163 | C2 | semidirect |
| 5. #26018348 | C2 | semidirect |
| 6. #26018340 | C2 | semidirect |
| 24. C2×D16×C89 | C4 | semidirect |
| 56. C2×D8×C89 | C2×C4 | semidirect |
| 63. C2×C16×C89 | C2×C4 | semidirect |
| 173. C89 | #13017 | semidirect |
| 179. C2×D16 | Dic89 | semidirect |
| 203. C2×D8 | C2×Dic89 | semidirect |
| 220. C2×C16 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029104 | 2 |
| C2×#19151411 | 2 |
| #26021968 | 2 |
| #26021163 | 2 |
| #26018348 | 2 |
| #26018340 | 2 |
| C22×D16×C89 | 2 |
| #13017 | 89 |