Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
434 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 4. C2×#89360 | C2 | semidirect |
| 5. #11729815 | C2 | semidirect |
| 6. #11727650 | C2 | semidirect |
| 7. #11727638 | C2 | semidirect |
| 13. C7×#495 | C4 | semidirect |
| 14. C7×#494 | C4 | semidirect |
| 132. #495 | Dic7 | semidirect |
| 133. #494 | Dic7 | semidirect |
| 317. C7 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3156 | 2 |
| #11729834 | 2 |
| #11729830 | 2 |
| C2×#89360 | 2 |
| #11729815 | 2 |
| #11727650 | 2 |
| #11727638 | 2 |
| #13216 | 7 |