Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
532 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 240 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 |
|---|---|---|
| 5. #10620893 | C2 | semidirect |
| 6. Dic3×Dic14 | C2 | semidirect |
| 10. C2×C3×Dic14 | C4 | semidirect |
| 40. C2×Dic14 | Dic3 | semidirect |
| 116. C3×C7 | #519 | semidirect |
| 151. C7 | #5812 | semidirect |
| 163. C3 | #90207 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic14 | 2 |
| #10621409 | 2 |
| C7×#926 | 2 |
| #10621090 | 2 |
| #10620893 | 2 |
| Dic3×Dic14 | 2 |
| #90207 | 3 |
| #5812 | 7 |