Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
204 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. C7×#890 | C2 | semidirect |
| 5. C7×#817 | C2 | semidirect |
| 6. C7×Dic3⋊C8 | C2 | semidirect |
| 7. C7×#807 | C2 | semidirect |
| 27. #4763 | C7 | direct (N × H) |
| 52. #890 | C2×C7 | semidirect |
| 55. #817 | C2×C7 | semidirect |
| 56. Dic3⋊C8 | C2×C7 | semidirect |
| 57. #807 | C2×C7 | semidirect |
| 127. C3×C7 | #478 | semidirect |
| 166. C7 | #4763 | direct (N × H) |
| 182. C3 | C7×#478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×Dic3 | 2 |
| C7×#890 | 2 |
| C3×C7×#102 | 2 |
| C7×#832 | 2 |
| C7×#817 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×#807 | 2 |
| C7×#478 | 3 |
| #4763 | 7 |