Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
396 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11727438 | C2 | semidirect |
| 4. #11727366 | C2 | semidirect |
| 5. #11725448 | C2 | semidirect |
| 7. #11725444 | C2 | semidirect |
| 338. C7 | #7834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2808 | 2 |
| #11727438 | 2 |
| #11727410 | 2 |
| #11727366 | 2 |
| #11725448 | 2 |
| #11725445 | 2 |
| #11725444 | 2 |
| #7834 | 7 |