Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 208 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×C7×#97 | 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. C7×#97 | D3 | semidirect |
| 22. #4717 | C7 | direct (N × H) |
| 44. #901 | C2×C7 | semidirect |
| 45. C3×#97 | C2×C7 | semidirect |
| 46. #819 | C2×C7 | semidirect |
| 47. #805 | C2×C7 | semidirect |
| 70. Dic12 | C4×C7 | semidirect |
| 71. D24 | C4×C7 | semidirect |
| 72. #204 | C4×C7 | semidirect |
| 82. #97 | D3×C7 | semidirect |
| 99. C3×C7 | #444 | semidirect |
| 129. C7 | #4717 | direct (N × H) |
| 139. C3 | C7×#444 | 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×C7×#97 | 2 |
| C7×#819 | 2 |
| C7×#805 | 2 |
| C7×#444 | 3 |
| #4717 | 7 |