Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
318 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 4. C7×#1365 | C2 | semidirect |
| 5. #11725608 | C2 | semidirect |
| 6. #11725371 | C2 | semidirect |
| 7. #11725282 | C2 | semidirect |
| 59. #1365 | D7 | semidirect |
| 230. C7 | #11975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#500 | 2 |
| #11727029 | 2 |
| #11726324 | 2 |
| C7×#1365 | 2 |
| #11725608 | 2 |
| #11725371 | 2 |
| #11725282 | 2 |
| #11975 | 7 |