Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
542 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #11740466 | C2 | semidirect |
| 5. #11729489 | C2 | semidirect |
| 6. #11727187 | C2 | semidirect |
| 7. #11725421 | C2 | semidirect |
| 332. C7 | #10097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2641 | 2 |
| #11740604 | 2 |
| #11740466 | 2 |
| #11729514 | 2 |
| #11729489 | 2 |
| #11727187 | 2 |
| #11725421 | 2 |
| #10097 | 7 |