Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 374 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 374 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×#948 | C2 | semidirect |
| 3. C2×C7×#208 | C2 | semidirect |
| 11. C7×#208 | C22 | semidirect |
| 12. C2×C7×C3⋊C8 | C22 | semidirect |
| 16. #5819 | C7 | direct (N × H) |
| 34. #948 | C2×C7 | semidirect |
| 35. C2×#208 | C2×C7 | semidirect |
| 57. #208 | C22×C7 | semidirect |
| 58. C2×C3⋊C8 | C22×C7 | semidirect |
| 79. C3×C7 | #568 | semidirect |
| 105. C7 | #5819 | direct (N × H) |
| 115. C3 | C7×#568 | 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 |
| C7×#948 | 2 |
| C2×C7×#208 | 2 |
| C7×#568 | 3 |
| #5819 | 7 |