Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
336 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 78 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. C7×#1004 | C2 | semidirect |
| 2. C3×C7×#127 | C2 | semidirect |
| 3. C7×#932 | C2 | semidirect |
| 4. C7×#833 | C2 | semidirect |
| 5. C7×#805 | C2 | semidirect |
| 9. C2×C3×C7×D4 | C22 | semidirect |
| 14. C3×C42×C7 | C22 | semidirect |
| 17. C7×#208 | C22 | semidirect |
| 20. C7×#127 | D3 | semidirect |
| 23. #5077 | C7 | direct (N × H) |
| 35. C7×D12 | D4 | semidirect |
| 37. C7×Dic6 | D4 | semidirect |
| 45. C2×C7×D4 | C2×D3 | semidirect |
| 49. C42×C7 | C2×D3 | semidirect |
| 50. #1004 | C2×C7 | semidirect |
| 51. C3×#127 | C2×C7 | semidirect |
| 52. #932 | C2×C7 | semidirect |
| 53. #833 | C2×C7 | semidirect |
| 54. #805 | C2×C7 | semidirect |
| 83. C2×C3×D4 | C22×C7 | semidirect |
| 88. C3×C42 | C22×C7 | semidirect |
| 91. #208 | C22×C7 | semidirect |
| 99. #127 | D3×C7 | semidirect |
| 123. D12 | C7×D4 | semidirect |
| 125. Dic6 | C7×D4 | semidirect |
| 127. C3×C7 | #453 | semidirect |
| 134. C2×D4 | C2×D3×C7 | semidirect |
| 138. C42 | C2×D3×C7 | semidirect |
| 169. C7 | #5077 | direct (N × H) |
| 185. C3 | C7×#453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1004 | 2 |
| C3×C7×#127 | 2 |
| C7×#932 | 2 |
| C7×#833 | 2 |
| C7×#805 | 2 |
| C7×#453 | 3 |
| #5077 | 7 |