Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 4. C7×#818 | C2 | semidirect |
| 5. C7×#817 | C2 | semidirect |
| 9. C3×C7×M16 | C4 | semidirect |
| 22. #5121 | C7 | direct (N × H) |
| 32. C3×C7×C8 | C2×C4 | semidirect |
| 35. C7×M16 | Dic3 | semidirect |
| 46. #818 | C2×C7 | semidirect |
| 47. #817 | C2×C7 | semidirect |
| 68. C7×C8 | C2×Dic3 | semidirect |
| 71. C3×M16 | C4×C7 | semidirect |
| 107. C3×C8 | C2×C4×C7 | semidirect |
| 108. C3×C7 | #428 | semidirect |
| 111. M16 | C7×Dic3 | semidirect |
| 142. C8 | C2×C7×Dic3 | semidirect |
| 143. C7 | #5121 | direct (N × H) |
| 158. C3 | C7×#428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×M16 | 2 |
| C7×#926 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C7×#818 | 2 |
| C7×#817 | 2 |
| C7×#428 | 3 |
| #5121 | 7 |