Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
256 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 64 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×#1142 | C2 | semidirect |
| 3. #10620893 | C2 | semidirect |
| 4. C2×#66566 | C2 | semidirect |
| 5. C7×#832 | C2 | semidirect |
| 6. #10620518 | C2 | semidirect |
| 7. #10620504 | C2 | semidirect |
| 23. C2×#1142 | D3 | semidirect |
| 44. C3×Dic14 | D4 | semidirect |
| 64. #832 | D7 | semidirect |
| 77. Dic21 | SD16 | semidirect |
| 95. Dic14 | #67 | semidirect |
| 153. C3×C7 | #460 | semidirect |
| 202. C7 | #5163 | semidirect |
| 221. C3 | #89534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621423 | 2 |
| C2×C3×#1142 | 2 |
| #10620893 | 2 |
| C2×#66566 | 2 |
| C7×#832 | 2 |
| #10620518 | 2 |
| #10620504 | 2 |
| #89534 | 3 |
| #5163 | 7 |