Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
196 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 196 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 |
|---|---|---|
| 1. D3×C7×D8 | C2 | semidirect |
| 2. C3×C7×D16 | C2 | semidirect |
| 3. C7×#826 | C2 | semidirect |
| 4. C7×D48 | C2 | semidirect |
| 5. D3×C7×C16 | C2 | semidirect |
| 8. C3×C7×D8 | C22 | semidirect |
| 10. C7×D24 | C22 | semidirect |
| 12. C3×C7×C16 | C22 | semidirect |
| 13. C7×C3⋊C16 | C22 | semidirect |
| 17. C7×D16 | D3 | direct (N × H) |
| 19. D3×D16 | C7 | direct (N × H) |
| 30. C7×D8 | C2×D3 | semidirect |
| 33. C7×C16 | C2×D3 | semidirect |
| 34. D3×D8 | C2×C7 | semidirect |
| 35. C3×D16 | C2×C7 | semidirect |
| 36. #826 | C2×C7 | semidirect |
| 37. D48 | C2×C7 | semidirect |
| 38. D3×C16 | C2×C7 | semidirect |
| 54. C3×D8 | C22×C7 | semidirect |
| 56. D24 | C22×C7 | semidirect |
| 58. C3×C16 | C22×C7 | semidirect |
| 59. C3⋊C16 | C22×C7 | semidirect |
| 63. D3×C7 | D16 | direct (N × H) |
| 67. D16 | D3×C7 | direct (N × H) |
| 82. C3×C7 | C2×D16 | semidirect |
| 86. D8 | C2×D3×C7 | semidirect |
| 89. C16 | C2×D3×C7 | semidirect |
| 107. C7 | D3×D16 | direct (N × H) |
| 111. D3 | C7×D16 | direct (N × H) |
| 118. C3 | C2×C7×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C7×D8 | 2 |
| C3×C7×D16 | 2 |
| C7×#826 | 2 |
| C7×D48 | 2 |
| D3×C7×C16 | 2 |
| C2×C7×D16 | 3 |
| D3×D16 | 7 |