Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
496 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 214 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×#1010 | C2 | semidirect |
| 2. C3×C7×#131 | C2 | semidirect |
| 3. C7×#909 | C2 | semidirect |
| 4. C2×C7×Dic12 | C2 | semidirect |
| 5. C7×#904 | C2 | semidirect |
| 22. C7×#131 | D3 | semidirect |
| 23. #5753 | C7 | direct (N × H) |
| 46. #1010 | C2×C7 | semidirect |
| 47. C3×#131 | C2×C7 | semidirect |
| 48. #909 | C2×C7 | semidirect |
| 49. C2×Dic12 | C2×C7 | semidirect |
| 50. #904 | C2×C7 | semidirect |
| 86. #131 | D3×C7 | semidirect |
| 103. C3×C7 | #578 | semidirect |
| 134. C7 | #5753 | direct (N × H) |
| 143. C3 | C7×#578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1010 | 2 |
| C3×C7×#131 | 2 |
| C7×#909 | 2 |
| C2×C7×Dic12 | 2 |
| C7×#904 | 2 |
| C7×#578 | 3 |
| #5753 | 7 |