Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 314 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. #11726846 | C2 | semidirect |
| 5. #11725331 | C2 | semidirect |
| 196. C7 | #11462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736093 | 2 |
| #11726846 | 2 |
| C7×#1315 | 2 |
| #11725495 | 2 |
| #11725331 | 2 |
| #11462 | 7 |