Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
292 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #11727650 | C2 | semidirect |
| 5. C7×#1378 | C2 | semidirect |
| 6. #11725628 | C2 | semidirect |
| 7. #11725627 | C2 | semidirect |
| 57. #1378 | D7 | semidirect |
| 237. C7 | #13490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89311 | 2 |
| #11729194 | 2 |
| #11727657 | 2 |
| #11727650 | 2 |
| C7×#1378 | 2 |
| #11725628 | 2 |
| #11725627 | 2 |
| #13490 | 7 |