Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
314 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 63 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. #11736978 | C2 | semidirect |
| 2. C7×#1687 | C2 | semidirect |
| 3. #11729047 | C2 | semidirect |
| 4. #11729043 | C2 | semidirect |
| 5. #11725567 | C2 | semidirect |
| 6. #11725274 | C2 | semidirect |
| 7. #11725271 | C2 | semidirect |
| 65. #1687 | D7 | semidirect |
| 280. C7 | #12348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736978 | 2 |
| C7×#1687 | 2 |
| #11729047 | 2 |
| #11729043 | 2 |
| #11725567 | 2 |
| #11725274 | 2 |
| #11725271 | 2 |
| #12348 | 7 |