Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
826 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 211 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. #11735936 | C2 | semidirect |
| 3. C7×#1745 | C2 | semidirect |
| 4. #11727595 | C2 | semidirect |
| 5. #11727149 | C2 | semidirect |
| 6. #11726449 | C2 | semidirect |
| 16. #89487 | C4 | semidirect |
| 17. #89484 | C4 | semidirect |
| 51. #1745 | D7 | semidirect |
| 198. C7 | #22283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735944 | 2 |
| #11735936 | 2 |
| C7×#1745 | 2 |
| #11727595 | 2 |
| #11727149 | 2 |
| #11726449 | 2 |
| #22283 | 7 |