Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
396 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11736711 | C2 | semidirect |
| 4. #11727555 | C2 | semidirect |
| 6. C7×#1275 | C2 | semidirect |
| 7. #11725553 | C2 | semidirect |
| 78. #1275 | D7 | semidirect |
| 302. C7 | #9284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736715 | 2 |
| #11736711 | 2 |
| #11728519 | 2 |
| #11727555 | 2 |
| #11727552 | 2 |
| C7×#1275 | 2 |
| #11725553 | 2 |
| #9284 | 7 |