Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
322 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 3. #11729064 | C2 | semidirect |
| 4. #11729062 | C2 | semidirect |
| 6. #11725370 | C2 | semidirect |
| 7. #11725364 | C2 | semidirect |
| 130. Dic14 | SD32 | semidirect |
| 240. C7 | #12356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×Dic14 | 2 |
| C7×#2208 | 2 |
| #11729064 | 2 |
| #11729062 | 2 |
| #11725569 | 2 |
| #11725370 | 2 |
| #11725364 | 2 |
| #12356 | 7 |