Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 134 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. C2×C7×#208 | C2 | semidirect |
| 3. C7×#836 | C2 | semidirect |
| 4. C7×#833 | C2 | semidirect |
| 20. #5237 | C7 | direct (N × H) |
| 45. C2×#208 | C2×C7 | semidirect |
| 46. #836 | C2×C7 | semidirect |
| 47. #833 | C2×C7 | semidirect |
| 111. C3×C7 | #413 | semidirect |
| 148. C7 | #5237 | direct (N × H) |
| 162. C3 | C7×#413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×#41 | 2 |
| C2×C7×#208 | 2 |
| C7×#836 | 2 |
| C7×#833 | 2 |
| C7×#413 | 3 |
| #5237 | 7 |