Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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×#1709 | C2 | semidirect |
| 2. #11729069 | C2 | semidirect |
| 4. C8×D56 | C2 | semidirect |
| 5. #11725599 | C2 | semidirect |
| 6. #11725596 | C2 | semidirect |
| 7. #11725246 | C2 | semidirect |
| 49. #1709 | D7 | semidirect |
| 217. C7 | #12428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1709 | 2 |
| #11729069 | 2 |
| #11729047 | 2 |
| C8×D56 | 2 |
| #11725599 | 2 |
| #11725596 | 2 |
| #11725246 | 2 |
| #12428 | 7 |