Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
420 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11729381 | C2 | semidirect |
| 5. #11729378 | C2 | semidirect |
| 6. #11728248 | C2 | semidirect |
| 7. #11725519 | C2 | semidirect |
| 336. C7 | #10466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3037 | 2 |
| #11729568 | 2 |
| #11729558 | 2 |
| #11729381 | 2 |
| #11729378 | 2 |
| #11728248 | 2 |
| #11725519 | 2 |
| #10466 | 7 |