Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 142 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×#835 | C2 | semidirect |
| 8. C2×C3×C7×Q8 | C4 | semidirect |
| 21. #5225 | C7 | direct (N × H) |
| 36. C2×C7×Q8 | Dic3 | semidirect |
| 48. #835 | C2×C7 | semidirect |
| 72. C2×C3×Q8 | C4×C7 | semidirect |
| 108. C3×C7 | #419 | semidirect |
| 111. C2×Q8 | C7×Dic3 | semidirect |
| 143. C7 | #5225 | direct (N × H) |
| 155. C3 | C7×#419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×Q8 | 2 |
| C7×#926 | 2 |
| C2×C7×#208 | 2 |
| C7×#835 | 2 |
| C7×#419 | 3 |
| #5225 | 7 |