Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 1. C2×D168 | C2 | semidirect |
| 2. C3×#6467 | C2 | semidirect |
| 3. C7×#812 | C2 | semidirect |
| 4. #10620478 | C2 | semidirect |
| 5. #10620473 | C2 | semidirect |
| 12. C3×Dic28 | C22 | semidirect |
| 13. C3×D56 | C22 | semidirect |
| 15. C7×C3⋊C16 | C22 | semidirect |
| 16. #6467 | D3 | semidirect |
| 35. Dic28 | C2×D3 | semidirect |
| 38. D56 | C2×D3 | semidirect |
| 45. #812 | D7 | semidirect |
| 72. C3⋊C16 | C2×D7 | semidirect |
| 99. C3×C7 | #509 | semidirect |
| 130. C7 | #5193 | semidirect |
| 142. C3 | #89680 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D168 | 2 |
| C3×#6467 | 2 |
| C7×#812 | 2 |
| #10620478 | 2 |
| #10620473 | 2 |
| #89680 | 3 |
| #5193 | 7 |