Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
496 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11730855 | C2 | semidirect |
| 5. #11728577 | C2 | semidirect |
| 6. #11728566 | C2 | semidirect |
| 7. #11725421 | C2 | semidirect |
| 323. C7 | #10093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740728 | 2 |
| #11740718 | 2 |
| #11730855 | 2 |
| C7×#1505 | 2 |
| #11728577 | 2 |
| #11728566 | 2 |
| #11725421 | 2 |
| #10093 | 7 |