Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 7. #66627 | C4 | semidirect |
| 14. C2×C3×C7⋊C8 | C4 | semidirect |
| 38. C2×C7⋊C8 | Dic3 | semidirect |
| 98. C3×C7 | #344 | semidirect |
| 132. C7 | #4556 | semidirect |
| 146. C3 | #89328 | 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×#1136 | 2 |
| #89328 | 3 |
| #4556 | 7 |