Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 1. C2×C7×Dic12 | C2 | semidirect |
| 4. C7×#869 | C2 | semidirect |
| 5. C3×C7×#97 | C2 | semidirect |
| 20. C7×#97 | D3 | semidirect |
| 21. #4715 | C7 | direct (N × H) |
| 41. C2×Dic12 | C2×C7 | semidirect |
| 44. #869 | C2×C7 | semidirect |
| 45. C3×#97 | C2×C7 | semidirect |
| 80. #97 | D3×C7 | semidirect |
| 98. C3×C7 | #497 | semidirect |
| 128. C7 | #4715 | direct (N × H) |
| 139. C3 | C7×#497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×Dic12 | 2 |
| C2×C7×#204 | 2 |
| C7×#875 | 2 |
| C7×#869 | 2 |
| C3×C7×#97 | 2 |
| C7×#497 | 3 |
| #4715 | 7 |