Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
464 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 79 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. C7×#1855 | C2 | semidirect |
| 3. #11729757 | C2 | semidirect |
| 5. #11727700 | C2 | semidirect |
| 7. #11725490 | C2 | semidirect |
| 78. #1855 | D7 | semidirect |
| 391. C7 | #10561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736087 | 2 |
| C7×#1855 | 2 |
| #11729757 | 2 |
| #11729744 | 2 |
| #11727700 | 2 |
| #11727675 | 2 |
| #11725490 | 2 |
| #10561 | 7 |