Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #11729042 | C2 | semidirect |
| 3. #11727031 | C2 | semidirect |
| 4. #11726332 | C2 | semidirect |
| 5. C7×#1361 | C2 | semidirect |
| 6. #11725370 | C2 | semidirect |
| 7. #11725275 | C2 | semidirect |
| 51. #1361 | D7 | semidirect |
| 207. C7 | #12467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11729042 | 2 |
| #11729036 | 2 |
| #11727031 | 2 |
| #11726332 | 2 |
| C7×#1361 | 2 |
| #11725370 | 2 |
| #11725275 | 2 |
| #12467 | 7 |