Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
482 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11739899 | C2 | semidirect |
| 5. #11729377 | C2 | semidirect |
| 6. #11725556 | C2 | semidirect |
| 7. #11725554 | C2 | semidirect |
| 11. C7×#477 | C4 | semidirect |
| 12. C7×#460 | C4 | semidirect |
| 125. #477 | Dic7 | semidirect |
| 126. #460 | Dic7 | semidirect |
| 334. C7 | #9330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3112 | 2 |
| #11739899 | 2 |
| #11729572 | 2 |
| #11729566 | 2 |
| #11729377 | 2 |
| #11725556 | 2 |
| #11725554 | 2 |
| #9330 | 7 |