Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
464 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. #11729251 | C2 | semidirect |
| 7. #11727110 | C2 | semidirect |
| 8. #11726990 | C2 | semidirect |
| 9. #11726966 | C2 | semidirect |
| 259. C7 | #33827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11738188 | 2 |
| C7×#2219 | 2 |
| #11729251 | 2 |
| #11729201 | 2 |
| #11729175 | 2 |
| #11728835 | 2 |
| #11727110 | 2 |
| #11726990 | 2 |
| #11726966 | 2 |
| #33827 | 7 |