Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 2. C2×C3×C4⋊Dic7 | C2 | semidirect |
| 5. C2×Dic3×Dic7 | C2 | semidirect |
| 6. C7×C3⋊#95 | C2 | semidirect |
| 7. #10620529 | C2 | semidirect |
| 16. #66631 | C4 | semidirect |
| 24. C2×C4⋊Dic7 | D3 | semidirect |
| 73. C3⋊#95 | D7 | semidirect |
| 194. C3×C7 | #388 | semidirect |
| 261. C7 | #4990 | semidirect |
| 290. C3 | #89442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66631 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| C2×#66575 | 2 |
| C2×Dic3×Dic7 | 2 |
| C7×C3⋊#95 | 2 |
| #10620529 | 2 |
| #89442 | 3 |
| #4990 | 7 |