Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
322 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 69 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. C7×#2241 | C2 | semidirect |
| 4. #11729062 | C2 | semidirect |
| 5. #11725607 | C2 | semidirect |
| 6. #11725312 | C2 | semidirect |
| 55. #2241 | D7 | semidirect |
| 130. Dic14 | SD32 | semidirect |
| 240. C7 | #12356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739397 | 2 |
| C7×#2241 | 2 |
| #11729069 | 2 |
| #11729062 | 2 |
| #11725607 | 2 |
| #11725312 | 2 |
| #11725310 | 2 |
| #12356 | 7 |