Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 228 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 |
|---|---|---|
| 3. C7×#818 | C2 | semidirect |
| 4. C7×#817 | C2 | semidirect |
| 7. C2×C3×C7×C8 | C4 | semidirect |
| 17. #5106 | C7 | direct (N × H) |
| 27. C2×C7×C8 | Dic3 | semidirect |
| 35. #818 | C2×C7 | semidirect |
| 36. #817 | C2×C7 | semidirect |
| 54. C2×C3×C8 | C4×C7 | semidirect |
| 82. C3×C7 | #427 | semidirect |
| 84. C2×C8 | C7×Dic3 | semidirect |
| 108. C7 | #5106 | direct (N × H) |
| 119. C3 | C7×#427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×C8 | 2 |
| C7×#926 | 2 |
| C7×#818 | 2 |
| C7×#817 | 2 |
| C7×#427 | 3 |
| #5106 | 7 |