Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
388 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 103 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. C7×#1568 | C2 | semidirect |
| 4. #11727486 | C2 | semidirect |
| 5. #11725564 | C2 | semidirect |
| 54. #1568 | D7 | semidirect |
| 238. C7 | #8630 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735903 | 2 |
| C7×#1568 | 2 |
| #11728565 | 2 |
| #11727486 | 2 |
| #11725564 | 2 |
| #8630 | 7 |