Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 66 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. C3×C7×Q32 | C2 | semidirect |
| 3. C7×#829 | C2 | semidirect |
| 4. C7×Dic24 | C2 | semidirect |
| 17. C7×Q32 | D3 | direct (N × H) |
| 19. D3×Q32 | C7 | direct (N × H) |
| 35. C3×Q32 | C2×C7 | semidirect |
| 36. #829 | C2×C7 | semidirect |
| 37. Dic24 | C2×C7 | semidirect |
| 60. D3×C7 | Q32 | direct (N × H) |
| 64. Q32 | D3×C7 | direct (N × H) |
| 78. C3×C7 | C2×Q32 | semidirect |
| 100. C7 | D3×Q32 | direct (N × H) |
| 102. D3 | C7×Q32 | direct (N × H) |
| 108. C3 | C2×C7×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C7×Q16 | 2 |
| C3×C7×Q32 | 2 |
| C7×#829 | 2 |
| C7×Dic24 | 2 |
| D3×C7×C16 | 2 |
| C2×C7×Q32 | 3 |
| D3×Q32 | 7 |