Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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. C3×C7×#127 | C2 | semidirect |
| 2. C2×C7×#213 | C2 | semidirect |
| 3. C4×C7×D12 | C2 | semidirect |
| 4. C7×#832 | C2 | semidirect |
| 5. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 18. C7×#127 | D3 | semidirect |
| 22. #5072 | C7 | direct (N × H) |
| 34. C7×D12 | D4 | semidirect |
| 47. C3×#127 | C2×C7 | semidirect |
| 48. C2×#213 | C2×C7 | semidirect |
| 49. C4×D12 | C2×C7 | semidirect |
| 50. #832 | C2×C7 | semidirect |
| 51. C4⋊(C3⋊C8) | C2×C7 | semidirect |
| 60. C3×C4×C7 | D8 | semidirect |
| 95. #127 | D3×C7 | semidirect |
| 108. C4×C7 | #213 | semidirect |
| 122. D12 | C7×D4 | semidirect |
| 125. C3×C7 | #459 | semidirect |
| 149. C3×C4 | C7×D8 | semidirect |
| 167. C7 | #5072 | direct (N × H) |
| 182. C4 | C7×#213 | semidirect |
| 185. C3 | C7×#459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#127 | 2 |
| C2×C7×#213 | 2 |
| C4×C7×D12 | 2 |
| C7×#832 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#459 | 3 |
| #5072 | 7 |