Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 51. C3×C4×C7 | Q16 | semidirect |
| 89. C4×C7 | Dic12 | semidirect |
| 106. C3×C7 | #462 | semidirect |
| 122. C3×C4 | Dic28 | semidirect |
| 139. C7 | #4849 | semidirect |
| 148. C4 | Dic84 | semidirect |
| 151. C3 | #89621 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic84 | 2 |
| #10621352 | 2 |
| C4×Dic42 | 2 |
| C3×C7×C4⋊C8 | 2 |
| #10620655 | 2 |
| #89621 | 3 |
| #4849 | 7 |