Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
428 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×C7×C82 | C2 | semidirect |
| 4. #11727480 | C2 | semidirect |
| 5. #11725462 | C2 | semidirect |
| 45. C2×C82 | D7 | semidirect |
| 183. C7 | #8187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735900 | 2 |
| C2×C7×C82 | 2 |
| #11727488 | 2 |
| #11727480 | 2 |
| #11725462 | 2 |
| #8187 | 7 |