Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 78 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×#1007 | C2 | semidirect |
| 2. C3×C7×#124 | C2 | semidirect |
| 3. C7×#932 | C2 | semidirect |
| 4. C7×#836 | C2 | semidirect |
| 5. C7×#805 | C2 | semidirect |
| 20. C7×#124 | D3 | semidirect |
| 23. #5062 | C7 | direct (N × H) |
| 49. #1007 | C2×C7 | semidirect |
| 50. C3×#124 | C2×C7 | semidirect |
| 51. #932 | C2×C7 | semidirect |
| 52. #836 | C2×C7 | semidirect |
| 53. #805 | C2×C7 | semidirect |
| 94. #124 | D3×C7 | semidirect |
| 119. C3×C7 | #454 | semidirect |
| 157. C7 | #5062 | direct (N × H) |
| 170. C3 | C7×#454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1007 | 2 |
| C3×C7×#124 | 2 |
| C7×#932 | 2 |
| C7×#836 | 2 |
| C7×#805 | 2 |
| C7×#454 | 3 |
| #5062 | 7 |