Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
570 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 4. #11727700 | C2 | semidirect |
| 5. #11725481 | C2 | semidirect |
| 17. #89758 | C4 | semidirect |
| 18. #89751 | C4 | semidirect |
| 19. #89721 | C4 | semidirect |
| 20. #89719 | C4 | semidirect |
| 350. C7 | #9383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2972 | 2 |
| #11739830 | 2 |
| #11729373 | 2 |
| #11727700 | 2 |
| #11725481 | 2 |
| #9383 | 7 |