Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
756 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 215 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. #11729844 | C2 | semidirect |
| 3. #11729843 | C2 | semidirect |
| 4. #11729571 | C2 | semidirect |
| 5. #11729517 | C2 | semidirect |
| 6. #11727625 | C2 | semidirect |
| 12. C7×#496 | C4 | semidirect |
| 13. C7×#493 | C4 | semidirect |
| 14. C7×#492 | C4 | semidirect |
| 30. C2×C7×SD16 | C2×C4 | semidirect |
| 31. C2×C7×D8 | C2×C4 | semidirect |
| 33. C7×C4⋊Q8 | C2×C4 | semidirect |
| 37. C7×#127 | C2×C4 | semidirect |
| 38. C7×#124 | C2×C4 | semidirect |
| 48. C7×#97 | C2×C4 | semidirect |
| 49. C4×C7×C8 | C2×C4 | semidirect |
| 101. #496 | Dic7 | semidirect |
| 102. #493 | Dic7 | semidirect |
| 103. #492 | Dic7 | semidirect |
| 145. C2×SD16 | C2×Dic7 | semidirect |
| 146. C2×D8 | C2×Dic7 | semidirect |
| 151. C4⋊Q8 | C2×Dic7 | semidirect |
| 155. #127 | C2×Dic7 | semidirect |
| 156. #124 | C2×Dic7 | semidirect |
| 167. #97 | C2×Dic7 | semidirect |
| 168. C4×C8 | C2×Dic7 | semidirect |
| 252. C7 | #23361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3151 | 2 |
| #11729844 | 2 |
| #11729843 | 2 |
| #11729571 | 2 |
| #11729517 | 2 |
| #11727625 | 2 |
| #23361 | 7 |