Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
424 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 99 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. #11740572 | C2 | semidirect |
| 3. #11729567 | C2 | semidirect |
| 4. #11729555 | C2 | semidirect |
| 5. #11729511 | C2 | semidirect |
| 6. #11725562 | C2 | semidirect |
| 7. #11725558 | C2 | semidirect |
| 10. C7×#497 | C4 | semidirect |
| 11. C7×#496 | C4 | semidirect |
| 12. C7×#491 | C4 | semidirect |
| 13. C7×#490 | C4 | semidirect |
| 148. #497 | Dic7 | semidirect |
| 149. #496 | Dic7 | semidirect |
| 150. #491 | Dic7 | semidirect |
| 151. #490 | Dic7 | semidirect |
| 381. C7 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3219 | 2 |
| #11740572 | 2 |
| #11729567 | 2 |
| #11729555 | 2 |
| #11729511 | 2 |
| #11725562 | 2 |
| #11725558 | 2 |
| #9370 | 7 |