Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
210 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 5. C7×#430 | C4 | semidirect |
| 9. C7×#338 | C4 | semidirect |
| 51. #430 | Dic7 | semidirect |
| 56. #338 | Dic7 | semidirect |
| 149. C7 | #7432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2091 | 2 |
| #11725489 | 2 |
| #11725487 | 2 |
| #7432 | 7 |