Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
650 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11739762 | C2 | semidirect |
| 3. #11729572 | C2 | semidirect |
| 4. #11729566 | C2 | semidirect |
| 5. #11729353 | C2 | semidirect |
| 6. #11725556 | C2 | semidirect |
| 7. #11725554 | C2 | semidirect |
| 12. C7×#476 | C4 | semidirect |
| 13. C7×#459 | C4 | semidirect |
| 35. C7×C4⋊Q8 | C2×C4 | semidirect |
| 36. C7×#127 | C2×C4 | semidirect |
| 57. C7×C4⋊C8 | C2×C4 | semidirect |
| 132. #476 | Dic7 | semidirect |
| 133. #459 | Dic7 | semidirect |
| 164. C7×D4 | #104 | semidirect |
| 200. C4⋊Q8 | C2×Dic7 | semidirect |
| 201. #127 | C2×Dic7 | semidirect |
| 222. C4⋊C8 | C2×Dic7 | semidirect |
| 331. D4 | #6411 | semidirect |
| 361. C7 | #9325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3109 | 2 |
| #11739762 | 2 |
| #11729572 | 2 |
| #11729566 | 2 |
| #11729353 | 2 |
| #11725556 | 2 |
| #11725554 | 2 |
| #9325 | 7 |