Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. #11729067 | C2 | semidirect |
| 3. #11729044 | C2 | semidirect |
| 4. #11725816 | C2 | semidirect |
| 5. #11725243 | C2 | semidirect |
| 33. #1709 | D7 | semidirect |
| 49. C7⋊C16 | D8 | semidirect |
| 126. C7 | #12519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1709 | 2 |
| #11729067 | 2 |
| #11729044 | 2 |
| #11725816 | 2 |
| #11725243 | 2 |
| #12519 | 7 |