Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
168 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 168 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. C3×C7×D16 | C2 | semidirect |
| 3. C7×#827 | C2 | semidirect |
| 4. C7×Dic24 | C2 | semidirect |
| 5. D3×C7×C16 | C2 | semidirect |
| 17. C7×D16 | D3 | semidirect |
| 19. #4912 | C7 | direct (N × H) |
| 34. #912 | C2×C7 | semidirect |
| 35. C3×D16 | C2×C7 | semidirect |
| 36. #827 | C2×C7 | semidirect |
| 37. Dic24 | C2×C7 | semidirect |
| 38. D3×C16 | C2×C7 | semidirect |
| 65. D16 | D3×C7 | semidirect |
| 79. C3×C7 | #508 | semidirect |
| 102. C7 | #4912 | direct (N × H) |
| 111. C3 | C7×#508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#912 | 2 |
| C3×C7×D16 | 2 |
| C7×#827 | 2 |
| C7×Dic24 | 2 |
| D3×C7×C16 | 2 |
| C7×#508 | 3 |
| #4912 | 7 |