Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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×#2155 | C2 | semidirect |
| 3. C2×#89308 | C2 | semidirect |
| 6. #11725539 | C2 | semidirect |
| 7. #11725532 | C2 | semidirect |
| 19. #89673 | C4 | semidirect |
| 58. #2155 | D7 | semidirect |
| 256. C7 | #12833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11739452 | 2 |
| C7×#2155 | 2 |
| C2×#89308 | 2 |
| #11728474 | 2 |
| #11728419 | 2 |
| #11725539 | 2 |
| #11725532 | 2 |
| #12833 | 7 |