Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
452 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11736499 | C2 | semidirect |
| 3. C7×#1963 | C2 | semidirect |
| 4. #11729557 | C2 | semidirect |
| 5. #11727185 | C2 | semidirect |
| 6. #11725516 | C2 | semidirect |
| 7. #11725421 | C2 | semidirect |
| 16. #89861 | C4 | semidirect |
| 17. #89852 | C4 | semidirect |
| 18. #89846 | C4 | semidirect |
| 19. #89843 | C4 | semidirect |
| 93. #1963 | D7 | semidirect |
| 402. C7 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11740737 | 2 |
| #11736499 | 2 |
| C7×#1963 | 2 |
| #11729557 | 2 |
| #11727185 | 2 |
| #11725516 | 2 |
| #11725421 | 2 |
| #8997 | 7 |