Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 3. #11728533 | C2 | semidirect |
| 4. #11727633 | C2 | semidirect |
| 6. C7×#1299 | C2 | semidirect |
| 7. C7⋊#1309 | C2 | semidirect |
| 81. #1299 | D7 | semidirect |
| 345. C7 | #9353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11736738 | 2 |
| #11736502 | 2 |
| #11728533 | 2 |
| #11727633 | 2 |
| #11727608 | 2 |
| C7×#1299 | 2 |
| C7⋊#1309 | 2 |
| #9353 | 7 |