Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1050 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 259 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. #11740617 | C2 | semidirect |
| 3. #11729791 | C2 | semidirect |
| 4. #11729519 | C2 | semidirect |
| 5. #11727517 | C2 | semidirect |
| 6. #11727505 | C2 | semidirect |
| 10. C7×#493 | C4 | semidirect |
| 25. C2×C7×D8 | C2×C4 | semidirect |
| 28. C7×#127 | C2×C4 | semidirect |
| 36. C4×C7×C8 | C2×C4 | semidirect |
| 74. #493 | Dic7 | semidirect |
| 109. C2×D8 | C2×Dic7 | semidirect |
| 113. #127 | C2×Dic7 | semidirect |
| 122. C4×C8 | C2×Dic7 | semidirect |
| 187. C7 | #22276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#493 | 2 |
| #11740617 | 2 |
| #11729791 | 2 |
| #11729519 | 2 |
| #11727517 | 2 |
| #11727505 | 2 |
| #22276 | 7 |