Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
574 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 574 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 |
|---|---|---|
| 2. #11739880 | C2 | semidirect |
| 3. C7×#1801 | C2 | semidirect |
| 5. #11725521 | C2 | semidirect |
| 51. #1801 | D7 | semidirect |
| 254. C7 | #9398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739921 | 2 |
| #11739880 | 2 |
| C7×#1801 | 2 |
| #11728256 | 2 |
| #11725521 | 2 |
| #9398 | 7 |