Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
314 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 314 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. C7×#1356 | C2 | semidirect |
| 4. #11725591 | C2 | semidirect |
| 5. #11725327 | C2 | semidirect |
| 49. #1356 | D7 | direct (N × H) |
| 179. D7 | #1356 | direct (N × H) |
| 200. C7 | C2×#1356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#491 | 2 |
| D7×#347 | 2 |
| C7×#1356 | 2 |
| #11725591 | 2 |
| #11725327 | 2 |
| C2×#1356 | 7 |