Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
362 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 109 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. C7×#1846 | C2 | semidirect |
| 4. #11725528 | C2 | semidirect |
| 5. #11725463 | C2 | semidirect |
| 40. #1846 | D7 | semidirect |
| 207. C7 | #13482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1846 | 2 |
| C2×#89286 | 2 |
| #11727530 | 2 |
| #11725528 | 2 |
| #11725463 | 2 |
| #13482 | 7 |