Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
308 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 16. C4⋊Dic21 | C4 | semidirect |
| 163. C3×C7 | #387 | semidirect |
| 217. C7 | #4654 | semidirect |
| 239. C3 | #89425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Dic21 | 2 |
| C2×#66577 | 2 |
| C2×Dic3×Dic7 | 2 |
| C7×C3⋊#95 | 2 |
| C3×C7⋊#95 | 2 |
| #10620529 | 2 |
| #89425 | 3 |
| #4654 | 7 |