Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
294 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 67 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. C22×Dic712 | C2 | semidirect |
| 2. C2×#19151436 | C2 | semidirect |
| 3. #26018432 | C2 | semidirect |
| 4. C22⋊#15667918 | C2 | semidirect |
| 24. Dic712 | D4 | semidirect |
| 79. C22×C89 | SD64 | semidirect |
| 97. C89 | #13662 | semidirect |
| 171. C22 | #19151436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic712 | 2 |
| C2×#19151436 | 2 |
| #26018432 | 2 |
| C22⋊#15667918 | 2 |
| C89×#2215 | 2 |
| #13662 | 89 |