Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 102 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. D3×C7×M16 | C2 | semidirect |
| 3. C3×C7×#100 | C2 | semidirect |
| 4. C7×#833 | C2 | semidirect |
| 5. C7×#824 | C2 | semidirect |
| 22. C7×#100 | D3 | semidirect |
| 23. #4745 | C7 | direct (N × H) |
| 50. D3×M16 | C2×C7 | semidirect |
| 51. C3×#100 | C2×C7 | semidirect |
| 52. #833 | C2×C7 | semidirect |
| 53. #824 | C2×C7 | semidirect |
| 97. #100 | D3×C7 | semidirect |
| 121. C3×C7 | #413 | semidirect |
| 160. C7 | #4745 | direct (N × H) |
| 174. C3 | C7×#413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#237 | 2 |
| D3×C7×M16 | 2 |
| C3×C7×#100 | 2 |
| C7×#833 | 2 |
| C7×#824 | 2 |
| C7×#413 | 3 |
| #4745 | 7 |