Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
308 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×#66627 | C2 | semidirect |
| 3. C3×#6489 | C2 | semidirect |
| 4. #10620514 | C2 | semidirect |
| 10. C7×#235 | C4 | semidirect |
| 12. C2×C7×D12 | C4 | semidirect |
| 14. C2×C7×Dic6 | C4 | semidirect |
| 16. #66627 | C22 | semidirect |
| 20. C3×C4×Dic7 | C22 | semidirect |
| 22. #6489 | D3 | semidirect |
| 56. C4×Dic7 | C2×D3 | semidirect |
| 100. #235 | Dic7 | semidirect |
| 102. C2×D12 | Dic7 | semidirect |
| 104. C2×Dic6 | Dic7 | semidirect |
| 151. C3×C7 | #421 | semidirect |
| 203. C7 | #5005 | semidirect |
| 221. C3 | #90008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C2×#66627 | 2 |
| C3×#6489 | 2 |
| #10620514 | 2 |
| #90008 | 3 |
| #5005 | 7 |