Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
434 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11728577 | C2 | semidirect |
| 5. #11728210 | C2 | semidirect |
| 6. #11725556 | C2 | semidirect |
| 7. #11725514 | C2 | semidirect |
| 20. #89837 | C4 | semidirect |
| 21. #89827 | C4 | semidirect |
| 362. C7 | #9377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2992 | 2 |
| #11740569 | 2 |
| #11729509 | 2 |
| #11728577 | 2 |
| #11728210 | 2 |
| #11725556 | 2 |
| #11725514 | 2 |
| #9377 | 7 |