Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 13. #89853 | C4 | semidirect |
| 14. #89851 | C4 | semidirect |
| 316. C7 | #9296 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740768 | 2 |
| #11730833 | 2 |
| C7×#1995 | 2 |
| #11729592 | 2 |
| #11728260 | 2 |
| #11725519 | 2 |
| #11725420 | 2 |
| #9296 | 7 |