Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
362 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 93 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. #11727596 | C2 | semidirect |
| 4. C7×#1281 | C2 | semidirect |
| 5. #11725544 | C2 | semidirect |
| 42. #1281 | D7 | semidirect |
| 202. C7 | #10631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11728528 | 2 |
| #11727596 | 2 |
| #11727577 | 2 |
| C7×#1281 | 2 |
| #11725544 | 2 |
| #10631 | 7 |