Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
356 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 168 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 |
|---|---|---|
| 10. C4×Dic21 | C4 | semidirect |
| 11. C4×C7×Dic3 | C4 | semidirect |
| 12. C3×C4×Dic7 | C4 | semidirect |
| 34. C4×Dic7 | Dic3 | semidirect |
| 64. C4×Dic3 | Dic7 | semidirect |
| 91. C3×C7 | #376 | semidirect |
| 121. C7 | #4932 | semidirect |
| 134. C3 | #89704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic21 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C3×C4×Dic7 | 2 |
| #10620529 | 2 |
| #89704 | 3 |
| #4932 | 7 |