Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
996 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 286 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. C22×C3×C7×D4 | C2 | semidirect |
| 2. C22×C7×#67 | C2 | semidirect |
| 3. C22×C7×D12 | C2 | semidirect |
| 4. C7×#940 | C2 | direct (N × H) |
| 5. C2×C4×C7×Dic3 | C2 | semidirect |
| 10. C2×C3×C7×D4 | C22 | semidirect |
| 13. C2×C7×#67 | C22 | semidirect |
| 16. C2×C7×D12 | C22 | semidirect |
| 17. C4×C7×Dic3 | C22 | semidirect |
| 20. C22×C7×D4 | D3 | semidirect |
| 23. C2×#940 | C7 | direct (N × H) |
| 32. C2×C3×C4×C7 | D4 | semidirect |
| 35. C2×C7×Dic3 | D4 | semidirect |
| 45. C2×C7×D4 | C2×D3 | semidirect |
| 49. C22×C3×D4 | C2×C7 | semidirect |
| 50. C22×#67 | C2×C7 | semidirect |
| 51. C22×D12 | C2×C7 | semidirect |
| 52. #940 | C2×C7 | direct (N × H) |
| 53. C2×C4×Dic3 | C2×C7 | semidirect |
| 63. C3×C4×C7 | C2×D4 | semidirect |
| 64. C7×Dic3 | C2×D4 | semidirect |
| 78. C2×C4×C7 | #67 | semidirect |
| 83. C2×C3×D4 | C22×C7 | semidirect |
| 86. C2×#67 | C22×C7 | semidirect |
| 89. C2×D12 | C22×C7 | semidirect |
| 90. C4×Dic3 | C22×C7 | semidirect |
| 92. C2×C3×C7 | #127 | semidirect |
| 98. C22×D4 | D3×C7 | semidirect |
| 111. C4×C7 | C2×#67 | semidirect |
| 120. C2×C3×C4 | C7×D4 | semidirect |
| 123. C2×Dic3 | C7×D4 | semidirect |
| 126. C3×C7 | C2×#127 | semidirect |
| 134. C2×D4 | C2×D3×C7 | semidirect |
| 140. C2×C7 | #940 | direct (N × H) |
| 152. C3×C4 | C2×C7×D4 | semidirect |
| 153. Dic3 | C2×C7×D4 | semidirect |
| 166. C2×C4 | C7×#67 | semidirect |
| 168. C7 | C2×#940 | direct (N × H) |
| 170. C2×C3 | C7×#127 | semidirect |
| 184. C4 | C2×C7×#67 | semidirect |
| 185. C3 | C2×C7×#127 | semidirect |
| 188. C2 | C7×#940 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×D4 | 2 |
| C22×C7×#67 | 2 |
| C22×C7×D12 | 2 |
| C7×#940 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C7×#127 | 3 |
| C2×#940 | 7 |