Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
214 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 85 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×#1371 | C2 | semidirect |
| 5. #11725307 | C2 | semidirect |
| 6. #11725276 | C2 | semidirect |
| 7. #11725275 | C2 | semidirect |
| 49. #1371 | D7 | semidirect |
| 188. C7 | #12035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11726806 | 2 |
| #11726324 | 2 |
| D7×#335 | 2 |
| C7×#1371 | 2 |
| #11725307 | 2 |
| #11725276 | 2 |
| #11725275 | 2 |
| #12035 | 7 |