Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 92 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. #66627 | C4 | semidirect |
| 11. C7×C4⋊Dic3 | C4 | semidirect |
| 14. C3×C4×Dic7 | C4 | semidirect |
| 36. C4×Dic7 | Dic3 | semidirect |
| 70. C4⋊Dic3 | Dic7 | semidirect |
| 103. C3×C7 | #339 | semidirect |
| 139. C7 | #4523 | semidirect |
| 154. C3 | #89327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66627 | 2 |
| C7×#926 | 2 |
| C2×C3×C4×Dic7 | 2 |
| #89327 | 3 |
| #4523 | 7 |