Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
562 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×C7×#500 | C2 | semidirect |
| 3. C2×#89341 | C2 | semidirect |
| 5. #11725460 | C2 | semidirect |
| 45. C2×#500 | D7 | semidirect |
| 238. C7 | #10278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#500 | 2 |
| C2×#89856 | 2 |
| C2×#89341 | 2 |
| #11727541 | 2 |
| #11725460 | 2 |
| #10278 | 7 |