Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
304 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 86 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×#951 | C2 | semidirect |
| 3. C7×#936 | C2 | semidirect |
| 4. C7×#837 | C2 | semidirect |
| 5. C7×#833 | C2 | semidirect |
| 12. C2×C7×Dic6 | C22 | semidirect |
| 16. C4×C7×Dic3 | C22 | semidirect |
| 17. C7×#208 | C22 | semidirect |
| 23. #5242 | C7 | direct (N × H) |
| 50. #951 | C2×C7 | semidirect |
| 51. #936 | C2×C7 | semidirect |
| 52. #837 | C2×C7 | semidirect |
| 53. #833 | C2×C7 | semidirect |
| 83. C2×Dic6 | C22×C7 | semidirect |
| 87. C4×Dic3 | C22×C7 | semidirect |
| 88. #208 | C22×C7 | semidirect |
| 121. C3×C7 | #455 | semidirect |
| 160. C7 | #5242 | direct (N × H) |
| 174. C3 | C7×#455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×H(5,𝔽2) | 2 |
| C7×#951 | 2 |
| C7×#936 | 2 |
| C7×#837 | 2 |
| C7×#833 | 2 |
| C7×#455 | 3 |
| #5242 | 7 |