Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
330 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 4. #11728360 | C2 | semidirect |
| 5. #11725623 | C2 | semidirect |
| 6. #11725616 | C2 | semidirect |
| 7. #11725529 | C2 | semidirect |
| 270. C7 | #13484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2139 | 2 |
| #11729838 | 2 |
| #11729832 | 2 |
| #11728360 | 2 |
| #11725623 | 2 |
| #11725616 | 2 |
| #11725529 | 2 |
| #13484 | 7 |