Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
406 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 406 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 |
|---|---|---|
| 4. #11727610 | C2 | semidirect |
| 5. #11727555 | C2 | semidirect |
| 6. #11725476 | C2 | semidirect |
| 7. #11725468 | C2 | semidirect |
| 338. C7 | #9314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2923 | 2 |
| #11739980 | 2 |
| #11729394 | 2 |
| #11727610 | 2 |
| #11727555 | 2 |
| #11725476 | 2 |
| #11725468 | 2 |
| #9314 | 7 |