Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
352 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 352 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 |
|---|---|---|
| 2. #11727038 | C2 | semidirect |
| 3. #11726323 | C2 | semidirect |
| 4. C7×#1365 | C2 | semidirect |
| 5. #11725608 | C2 | semidirect |
| 6. #11725366 | C2 | semidirect |
| 7. #11725279 | C2 | semidirect |
| 58. #1365 | D7 | semidirect |
| 251. C7 | #11986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739378 | 2 |
| #11727038 | 2 |
| #11726323 | 2 |
| C7×#1365 | 2 |
| #11725608 | 2 |
| #11725366 | 2 |
| #11725279 | 2 |
| #11986 | 7 |