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×C7×#214 | C2 | semidirect |
| 3. #10620906 | C2 | semidirect |
| 4. C2×#66568 | C2 | semidirect |
| 5. C3×#6406 | C2 | semidirect |
| 6. #10620518 | C2 | semidirect |
| 7. #10620503 | C2 | semidirect |
| 26. #6406 | D3 | semidirect |
| 43. C7×Dic6 | D4 | semidirect |
| 61. C2×#214 | D7 | semidirect |
| 77. Dic21 | SD16 | semidirect |
| 150. Dic6 | C22⋊D7 | semidirect |
| 153. C3×C7 | #460 | semidirect |
| 202. C7 | #4762 | semidirect |
| 221. C3 | #89935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621423 | 2 |
| C2×C7×#214 | 2 |
| #10620906 | 2 |
| C2×#66568 | 2 |
| C3×#6406 | 2 |
| #10620518 | 2 |
| #10620503 | 2 |
| #89935 | 3 |
| #4762 | 7 |