Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
388 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 12. C4×C7×Dic3 | C4 | semidirect |
| 13. Dic3⋊Dic7 | C4 | semidirect |
| 56. C7×Dic3 | C42 | semidirect |
| 57. C7×Dic3 | C4⋊C4 | semidirect |
| 80. C4×Dic3 | Dic7 | semidirect |
| 115. C3×C7 | C4×C4⋊C4 | semidirect |
| 137. Dic3 | C4×Dic7 | semidirect |
| 138. Dic3 | C4⋊Dic7 | semidirect |
| 153. C7 | #4649 | semidirect |
| 169. C3 | C4×C4⋊Dic7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×Dic3 | 2 |
| C2×Dic3⋊Dic7 | 2 |
| C2×Dic3×Dic7 | 2 |
| #10620670 | 2 |
| C3×C7⋊#95 | 2 |
| C4×C4⋊Dic7 | 3 |
| #4649 | 7 |