Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 2. #11740366 | C2 | semidirect |
| 3. #11729464 | C2 | semidirect |
| 4. #11729430 | C2 | semidirect |
| 5. #11729428 | C2 | semidirect |
| 6. #11725493 | C2 | semidirect |
| 7. #11725492 | C2 | semidirect |
| 10. C7×#483 | C4 | semidirect |
| 12. C7×#480 | C4 | semidirect |
| 15. C7×#450 | C4 | semidirect |
| 17. C7×#447 | C4 | semidirect |
| 152. #483 | Dic7 | semidirect |
| 154. #480 | Dic7 | semidirect |
| 157. #450 | Dic7 | semidirect |
| 159. #447 | Dic7 | semidirect |
| 415. C7 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3194 | 2 |
| #11740366 | 2 |
| #11729464 | 2 |
| #11729430 | 2 |
| #11729428 | 2 |
| #11725493 | 2 |
| #11725492 | 2 |
| #9332 | 7 |