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. C7×#940 | C2 | semidirect |
| 3. C7×#908 | C2 | semidirect |
| 4. C3×C7×#100 | C2 | semidirect |
| 5. C7×#825 | C2 | semidirect |
| 13. C2×C7×D12 | C22 | semidirect |
| 14. C3×C7×M16 | C22 | semidirect |
| 15. C4×C7×Dic3 | C22 | semidirect |
| 22. C7×#100 | D3 | semidirect |
| 23. #4747 | C7 | direct (N × H) |
| 35. C7×D12 | D4 | semidirect |
| 37. C7×Dic6 | D4 | semidirect |
| 48. C7×M16 | C2×D3 | semidirect |
| 50. #1004 | C2×C7 | semidirect |
| 51. #940 | C2×C7 | semidirect |
| 52. #908 | C2×C7 | semidirect |
| 53. C3×#100 | C2×C7 | semidirect |
| 54. #825 | C2×C7 | semidirect |
| 87. C2×D12 | C22×C7 | semidirect |
| 88. C3×M16 | C22×C7 | semidirect |
| 89. C4×Dic3 | C22×C7 | semidirect |
| 101. #100 | D3×C7 | semidirect |
| 123. D12 | C7×D4 | semidirect |
| 125. Dic6 | C7×D4 | semidirect |
| 127. C3×C7 | #453 | semidirect |
| 137. M16 | C2×D3×C7 | semidirect |
| 169. C7 | #4747 | 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 |
| C7×#940 | 2 |
| C7×#908 | 2 |
| C3×C7×#100 | 2 |
| C7×#825 | 2 |
| C7×#453 | 3 |
| #4747 | 7 |