Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
356 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 206 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 |
|---|---|---|
| 8. C3×C42×C7 | C4 | semidirect |
| 9. C4×C7×Dic3 | C4 | semidirect |
| 13. #4932 | C7 | direct (N × H) |
| 25. C42×C7 | Dic3 | semidirect |
| 46. C3×C42 | C4×C7 | semidirect |
| 47. C4×Dic3 | C4×C7 | semidirect |
| 67. C3×C7 | #376 | semidirect |
| 72. C42 | C7×Dic3 | semidirect |
| 89. C7 | #4932 | direct (N × H) |
| 99. C3 | C7×#376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C7 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#376 | 3 |
| #4932 | 7 |