Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 62 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×#912 | C2 | semidirect |
| 2. D3×C7×D8 | C2 | semidirect |
| 3. C3×C7×D16 | C2 | semidirect |
| 4. C7×#827 | C2 | semidirect |
| 5. C7×#826 | C2 | semidirect |
| 6. C7×#800 | C2 | semidirect |
| 7. C7×#798 | C2 | semidirect |
| 12. C3×C7×D8 | C22 | semidirect |
| 15. C7×Dic12 | C22 | semidirect |
| 18. C3×C7×C16 | C22 | semidirect |
| 19. C7×C3⋊C16 | C22 | semidirect |
| 25. C7×D16 | D3 | semidirect |
| 27. #4911 | C7 | direct (N × H) |
| 46. C7×D8 | C2×D3 | semidirect |
| 49. C7×C16 | C2×D3 | semidirect |
| 50. #912 | C2×C7 | semidirect |
| 51. D3×D8 | C2×C7 | semidirect |
| 52. C3×D16 | C2×C7 | semidirect |
| 53. #827 | C2×C7 | semidirect |
| 54. #826 | C2×C7 | semidirect |
| 55. #800 | C2×C7 | semidirect |
| 56. #798 | C2×C7 | semidirect |
| 80. C3×D8 | C22×C7 | semidirect |
| 83. Dic12 | C22×C7 | semidirect |
| 86. C3×C16 | C22×C7 | semidirect |
| 87. C3⋊C16 | C22×C7 | semidirect |
| 98. D16 | D3×C7 | semidirect |
| 119. C3×C7 | #509 | semidirect |
| 127. D8 | C2×D3×C7 | semidirect |
| 130. C16 | C2×D3×C7 | semidirect |
| 155. C7 | #4911 | direct (N × H) |
| 169. C3 | C7×#509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#912 | 2 |
| D3×C7×D8 | 2 |
| C3×C7×D16 | 2 |
| C7×#827 | 2 |
| C7×#826 | 2 |
| C7×#800 | 2 |
| C7×#798 | 2 |
| C7×#509 | 3 |
| #4911 | 7 |