Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
394 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 115 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. C7×#2162 | C2 | semidirect |
| 3. C4×#6392 | C2 | semidirect |
| 4. #11725332 | C2 | semidirect |
| 11. #89467 | C4 | semidirect |
| 14. C4×D56 | C4 | semidirect |
| 15. #89454 | C4 | semidirect |
| 48. #2162 | D7 | semidirect |
| 237. C7 | #11742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735915 | 2 |
| C7×#2162 | 2 |
| C4×#6392 | 2 |
| #11725332 | 2 |
| #11742 | 7 |