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. #10620906 | C2 | semidirect |
| 6. Dic6×Dic7 | C2 | semidirect |
| 10. C2×C7×Dic6 | C4 | semidirect |
| 78. C2×Dic6 | Dic7 | semidirect |
| 116. C3×C7 | #519 | semidirect |
| 151. C7 | #5516 | semidirect |
| 163. C3 | #90503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Dic6 | 2 |
| #10621409 | 2 |
| C3×#6489 | 2 |
| #10621091 | 2 |
| #10620906 | 2 |
| Dic6×Dic7 | 2 |
| #90503 | 3 |
| #5516 | 7 |