Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
308 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 2. C3×C7×#117 | C2 | semidirect |
| 3. C2×C7×#208 | C2 | semidirect |
| 4. C7×#805 | C2 | semidirect |
| 10. C7×#235 | C4 | semidirect |
| 12. C2×C7×D12 | C4 | semidirect |
| 14. C2×C7×Dic6 | C4 | semidirect |
| 17. C3×C42×C7 | C22 | semidirect |
| 19. C7×#208 | C22 | semidirect |
| 23. C7×#117 | D3 | semidirect |
| 25. #5005 | C7 | direct (N × H) |
| 59. C42×C7 | C2×D3 | semidirect |
| 61. C3×#117 | C2×C7 | semidirect |
| 62. C2×#208 | C2×C7 | semidirect |
| 63. #805 | C2×C7 | semidirect |
| 100. #235 | C4×C7 | semidirect |
| 102. C2×D12 | C4×C7 | semidirect |
| 104. C2×Dic6 | C4×C7 | semidirect |
| 107. C3×C42 | C22×C7 | semidirect |
| 109. #208 | C22×C7 | semidirect |
| 118. #117 | D3×C7 | semidirect |
| 151. C3×C7 | #421 | semidirect |
| 166. C42 | C2×D3×C7 | semidirect |
| 203. C7 | #5005 | direct (N × H) |
| 221. C3 | C7×#421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C3×C7×#117 | 2 |
| C2×C7×#208 | 2 |
| C7×#805 | 2 |
| C7×#421 | 3 |
| #5005 | 7 |