Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
306 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11727498 | C2 | semidirect |
| 3. #11727483 | C2 | semidirect |
| 4. #11725605 | C2 | semidirect |
| 5. #11725602 | C2 | semidirect |
| 250. C7 | #11943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3168 | 2 |
| #11727498 | 2 |
| #11727483 | 2 |
| #11725605 | 2 |
| #11725602 | 2 |
| #11943 | 7 |