Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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. D7×#499 | C2 | semidirect |
| 3. C7×#2244 | C2 | semidirect |
| 4. #11729107 | C2 | semidirect |
| 5. #11729043 | C2 | semidirect |
| 6. #11726943 | C2 | semidirect |
| 7. #11726938 | C2 | semidirect |
| 8. #11726837 | C2 | semidirect |
| 9. #11726825 | C2 | semidirect |
| 77. #2244 | D7 | semidirect |
| 279. C7 | #33708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D7×#499 | 2 |
| #11739227 | 2 |
| C7×#2244 | 2 |
| #11729107 | 2 |
| #11729043 | 2 |
| #11726943 | 2 |
| #11726938 | 2 |
| #11726837 | 2 |
| #11726825 | 2 |
| #33708 | 7 |