Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
794 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 151 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. #11729393 | C2 | semidirect |
| 3. #11729392 | C2 | semidirect |
| 4. #11729368 | C2 | semidirect |
| 5. #11729355 | C2 | semidirect |
| 357. C7 | #8320 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3460 | 2 |
| #11729393 | 2 |
| #11729392 | 2 |
| #11729368 | 2 |
| #11729355 | 2 |
| #8320 | 7 |