Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
286 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11727625 | C2 | semidirect |
| 3. #11727618 | C2 | semidirect |
| 4. #11725587 | C2 | semidirect |
| 5. #11725586 | C2 | semidirect |
| 9. C7×#499 | C4 | semidirect |
| 10. C7×#495 | C4 | semidirect |
| 15. C7×#442 | C4 | semidirect |
| 16. C7×#441 | C4 | semidirect |
| 105. #499 | Dic7 | semidirect |
| 106. #495 | Dic7 | semidirect |
| 111. #442 | Dic7 | semidirect |
| 112. #441 | Dic7 | semidirect |
| 259. C7 | #11836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3183 | 2 |
| #11727625 | 2 |
| #11727618 | 2 |
| #11725587 | 2 |
| #11725586 | 2 |
| #11725585 | 2 |
| #11725584 | 2 |
| #11836 | 7 |