Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
348 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 348 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. #11726806 | C2 | semidirect |
| 3. #11726321 | C2 | semidirect |
| 4. C7×#1331 | C2 | semidirect |
| 5. #11725569 | C2 | semidirect |
| 6. #11725310 | C2 | semidirect |
| 7. #11725277 | C2 | semidirect |
| 67. #1331 | D7 | semidirect |
| 300. C7 | #11649 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11737043 | 2 |
| #11726806 | 2 |
| #11726321 | 2 |
| C7×#1331 | 2 |
| #11725569 | 2 |
| #11725310 | 2 |
| #11725277 | 2 |
| #11649 | 7 |