Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
212 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 212 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 |
|---|---|---|
| 2. C7×#901 | C2 | semidirect |
| 3. C3×C4×C7×C8 | C2 | semidirect |
| 4. C7×#819 | C2 | semidirect |
| 5. C7×#805 | C2 | semidirect |
| 12. C7×Dic12 | C4 | semidirect |
| 13. C7×D24 | C4 | semidirect |
| 14. C7×#204 | C4 | semidirect |
| 21. C4×C7×C8 | D3 | semidirect |
| 22. #4700 | C7 | direct (N × H) |
| 45. #901 | C2×C7 | semidirect |
| 46. C3×C4×C8 | C2×C7 | semidirect |
| 47. #819 | C2×C7 | semidirect |
| 48. #805 | C2×C7 | semidirect |
| 72. Dic12 | C4×C7 | semidirect |
| 73. D24 | C4×C7 | semidirect |
| 74. #204 | C4×C7 | semidirect |
| 84. C4×C8 | D3×C7 | semidirect |
| 102. C3×C7 | #443 | semidirect |
| 133. C7 | #4700 | direct (N × H) |
| 143. C3 | C7×#443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#904 | 2 |
| C7×#901 | 2 |
| C3×C4×C7×C8 | 2 |
| C7×#819 | 2 |
| C7×#805 | 2 |
| C7×#443 | 3 |
| #4700 | 7 |