Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
560 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 1. C2×D3×Dic14 | C2 | semidirect |
| 2. #10621352 | C2 | semidirect |
| 4. C3×C4×Dic14 | C2 | semidirect |
| 5. #10621030 | C2 | semidirect |
| 6. #10620979 | C2 | semidirect |
| 8. #10620927 | C2 | semidirect |
| 34. C4×Dic14 | D3 | semidirect |
| 43. C7×D12 | Q8 | semidirect |
| 47. C3×Dic14 | D4 | semidirect |
| 78. C2×D3×C7 | C2×Q8 | semidirect |
| 81. C3×C4×C7 | C2×Q8 | semidirect |
| 100. Dic14 | D12 | direct (N × H) |
| 137. C4×C7 | D3×Q8 | semidirect |
| 150. D12 | Dic14 | direct (N × H) |
| 155. C3×C7 | D4×Q8 | semidirect |
| 180. C2×D3 | C2×Dic14 | semidirect |
| 184. C3×C4 | C2×Dic14 | semidirect |
| 202. C7 | Q8×D12 | semidirect |
| 216. C4 | D3×Dic14 | semidirect |
| 218. C3 | D4×Dic14 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Dic14 | 2 |
| #10621352 | 2 |
| C4×C7×D12 | 2 |
| C3×C4×Dic14 | 2 |
| #10621030 | 2 |
| #10620979 | 2 |
| D12×Dic7 | 2 |
| #10620927 | 2 |
| D4×Dic14 | 3 |
| Q8×D12 | 7 |