Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 10. #89471 | C4 | semidirect |
| 12. C4×Dic28 | C4 | semidirect |
| 13. #89454 | C4 | semidirect |
| 220. C7 | #11857 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11735920 | 2 |
| C7×#2162 | 2 |
| #11727516 | 2 |
| #11725334 | 2 |
| #11857 | 7 |