Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 70 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×#904 | C2 | semidirect |
| 2. C2×C7×D24 | C2 | semidirect |
| 3. C3×C7×M32 | C2 | semidirect |
| 4. C7×#800 | C2 | semidirect |
| 5. C7×D48 | C2 | semidirect |
| 10. C7×Dic12 | C22 | semidirect |
| 13. C7×D24 | C22 | semidirect |
| 15. C3×C7×C16 | C22 | semidirect |
| 20. C7×M32 | D3 | semidirect |
| 21. #4908 | C7 | direct (N × H) |
| 40. C7×C16 | C2×D3 | semidirect |
| 41. #904 | C2×C7 | semidirect |
| 42. C2×D24 | C2×C7 | semidirect |
| 43. C3×M32 | C2×C7 | semidirect |
| 44. #800 | C2×C7 | semidirect |
| 45. D48 | C2×C7 | semidirect |
| 67. Dic12 | C22×C7 | semidirect |
| 70. D24 | C22×C7 | semidirect |
| 72. C3×C16 | C22×C7 | semidirect |
| 81. M32 | D3×C7 | semidirect |
| 99. C3×C7 | #509 | semidirect |
| 108. C16 | C2×D3×C7 | semidirect |
| 130. C7 | #4908 | direct (N × H) |
| 142. C3 | C7×#509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#904 | 2 |
| C2×C7×D24 | 2 |
| C3×C7×M32 | 2 |
| C7×#800 | 2 |
| C7×D48 | 2 |
| C7×#509 | 3 |
| #4908 | 7 |