Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11731710 | C2 | semidirect |
| 5. #11728577 | C2 | semidirect |
| 6. #11725558 | C2 | semidirect |
| 7. #11725439 | C2 | semidirect |
| 13. #89853 | C4 | semidirect |
| 14. #89842 | C4 | semidirect |
| 278. C7 | #9430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740728 | 2 |
| #11731710 | 2 |
| C7×#1514 | 2 |
| #11729567 | 2 |
| #11728577 | 2 |
| #11725558 | 2 |
| #11725439 | 2 |
| #9430 | 7 |