Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
314 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 91 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×#2150 | C2 | semidirect |
| 4. #11729181 | C2 | semidirect |
| 6. #11727548 | C2 | semidirect |
| 7. #11725627 | C2 | semidirect |
| 57. #2150 | D7 | semidirect |
| 263. C7 | #13466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2150 | 2 |
| #11729204 | 2 |
| #11729202 | 2 |
| #11729181 | 2 |
| #11727549 | 2 |
| #11727548 | 2 |
| #11725627 | 2 |
| #13466 | 7 |