Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 284 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 |
|---|---|---|
| 6. C22×Dic21 | C4 | semidirect |
| 12. C7×#217 | C4 | semidirect |
| 14. C3×C22⋊Dic7 | C4 | semidirect |
| 42. C22⋊Dic7 | Dic3 | semidirect |
| 87. #217 | Dic7 | semidirect |
| 130. C3×C7 | #342 | semidirect |
| 180. C7 | #4527 | semidirect |
| 206. C3 | #89322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66636 | 2 |
| C2×C7×#217 | 2 |
| C2×C3×C22⋊Dic7 | 2 |
| #89322 | 3 |
| #4527 | 7 |