Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 4. C7×Dic3⋊C8 | C2 | semidirect |
| 5. C7×C8×Dic3 | C2 | semidirect |
| 21. #4718 | C7 | direct (N × H) |
| 27. C2×C7×Dic3 | C8 | semidirect |
| 46. Dic3⋊C8 | C2×C7 | semidirect |
| 47. C8×Dic3 | C2×C7 | semidirect |
| 104. C2×Dic3 | C7×C8 | semidirect |
| 111. C3×C7 | #431 | semidirect |
| 147. C7 | #4718 | direct (N × H) |
| 162. C3 | C7×#431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×Dic3 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C7×#830 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×C8×Dic3 | 2 |
| C7×#431 | 3 |
| #4718 | 7 |