Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1050 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 227 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. #11730834 | C2 | semidirect |
| 3. C7×#1746 | C2 | semidirect |
| 4. #11727577 | C2 | semidirect |
| 5. #11727517 | C2 | semidirect |
| 6. #11726427 | C2 | semidirect |
| 16. #89467 | C4 | semidirect |
| 32. C2×D56 | C2×C4 | semidirect |
| 34. #6437 | C2×C4 | semidirect |
| 37. C4×C7×C8 | C2×C4 | semidirect |
| 46. #1746 | D7 | semidirect |
| 122. C4×C8 | C4×D7 | semidirect |
| 187. C7 | #22276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89467 | 2 |
| #11730834 | 2 |
| C7×#1746 | 2 |
| #11727577 | 2 |
| #11727517 | 2 |
| #11726427 | 2 |
| #22276 | 7 |