Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
682 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 155 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. #11739361 | C2 | semidirect |
| 3. C7×#2244 | C2 | semidirect |
| 4. #11729106 | C2 | semidirect |
| 5. #11729043 | C2 | semidirect |
| 6. #11726944 | C2 | semidirect |
| 7. #11726937 | C2 | semidirect |
| 8. #11726834 | C2 | semidirect |
| 9. #11726825 | C2 | semidirect |
| 14. C7×#499 | C22 | semidirect |
| 22. #89646 | C22 | semidirect |
| 27. #89455 | C22 | semidirect |
| 28. C7×#357 | C22 | semidirect |
| 29. C7×#346 | C22 | semidirect |
| 30. #89357 | C22 | semidirect |
| 31. #89304 | C22 | semidirect |
| 32. C16×Dic7 | C22 | semidirect |
| 33. #89286 | C22 | semidirect |
| 34. #89256 | C22 | semidirect |
| 77. #2244 | D7 | semidirect |
| 126. #499 | C2×D7 | semidirect |
| 139. #357 | C2×D7 | semidirect |
| 141. #346 | C2×D7 | semidirect |
| 290. C7 | #33704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739361 | 2 |
| D7×#493 | 2 |
| C7×#2244 | 2 |
| #11729106 | 2 |
| #11729043 | 2 |
| #11726944 | 2 |
| #11726937 | 2 |
| #11726834 | 2 |
| #11726825 | 2 |
| #33704 | 7 |