Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 60 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. #10621030 | C2 | semidirect |
| 3. #10620674 | C2 | semidirect |
| 4. C7×#835 | C2 | semidirect |
| 7. #10620487 | C2 | semidirect |
| 56. #835 | D7 | semidirect |
| 133. C3×C7 | #489 | semidirect |
| 174. C7 | #5055 | semidirect |
| 190. C3 | #89567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6510 | 2 |
| #10621030 | 2 |
| #10620674 | 2 |
| C7×#835 | 2 |
| #10620500 | 2 |
| #10620499 | 2 |
| #10620487 | 2 |
| #89567 | 3 |
| #5055 | 7 |