Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
524 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. #11740652 | C2 | semidirect |
| 5. #11729533 | C2 | semidirect |
| 6. #11728546 | C2 | semidirect |
| 7. #11725550 | C2 | semidirect |
| 129. #1136 | SD16 | semidirect |
| 350. C7 | #10197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3206 | 2 |
| #11740765 | 2 |
| #11740652 | 2 |
| #11729572 | 2 |
| #11729533 | 2 |
| #11728546 | 2 |
| #11725550 | 2 |
| #10197 | 7 |