Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
502 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 139 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×#19151426 | C2 | semidirect |
| 2. C2×#19151399 | C2 | semidirect |
| 3. C2×#19151373 | C2 | semidirect |
| 4. #26021119 | C2 | semidirect |
| 17. C2×D16×C89 | C4 | semidirect |
| 72. C16×C89 | C22⋊C4 | semidirect |
| 124. C89 | #13239 | semidirect |
| 128. C2×D16 | Dic89 | semidirect |
| 191. C16 | C22⋊Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151426 | 2 |
| C2×#19151399 | 2 |
| C2×#19151373 | 2 |
| #26021119 | 2 |
| C22×D16×C89 | 2 |
| #13239 | 89 |