Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 232 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×C4×C7×Dic3 | C2 | semidirect |
| 3. C2×C3×C4×Dic7 | C2 | semidirect |
| 4. C2×#66577 | C2 | semidirect |
| 6. #10620948 | C2 | direct (N × H) |
| 11. C2×C4×D21 | C4 | semidirect |
| 15. C4×C7×Dic3 | C22 | semidirect |
| 16. C3×C4×Dic7 | C22 | semidirect |
| 17. #66577 | C22 | semidirect |
| 23. C2×C4×Dic7 | D3 | semidirect |
| 34. C4×D21 | C2×C4 | semidirect |
| 49. C4×Dic7 | C2×D3 | semidirect |
| 54. C2×C4×Dic3 | D7 | semidirect |
| 90. C4×Dic3 | C2×D7 | semidirect |
| 91. C2×C3×C7 | #117 | semidirect |
| 124. C3×C7 | C2×#117 | semidirect |
| 136. C2×C7 | #872 | semidirect |
| 163. C7 | C2×#872 | semidirect |
| 164. C2×C3 | #6435 | semidirect |
| 178. C3 | C2×#6435 | semidirect |
| 180. C2 | #10620948 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D21 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C2×#66577 | 2 |
| C2×#66575 | 2 |
| #10620948 | 2 |
| C2×#6435 | 3 |
| C2×#872 | 7 |