Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 254 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. C22×C3×Dic14 | C2 | semidirect |
| 3. C2×C3×C22⋊Dic7 | C2 | semidirect |
| 4. C3×#6499 | C2 | direct (N × H) |
| 5. C2×C3×C4×Dic7 | C2 | semidirect |
| 6. C2×#6499 | C3 | direct (N × H) |
| 14. C2×C3×Dic14 | C22 | semidirect |
| 15. C3×C22⋊Dic7 | C22 | semidirect |
| 16. C3×C4×Dic7 | C22 | semidirect |
| 18. C22×Dic14 | C2×C3 | semidirect |
| 19. C2×C22⋊Dic7 | C2×C3 | semidirect |
| 20. #6499 | C2×C3 | direct (N × H) |
| 21. C2×C4×Dic7 | C2×C3 | semidirect |
| 42. C2×Dic14 | C22×C3 | semidirect |
| 43. C22⋊Dic7 | C22×C3 | semidirect |
| 44. C4×Dic7 | C22×C3 | semidirect |
| 83. C2×C3×C7 | #124 | semidirect |
| 112. C3×C7 | C2×#124 | semidirect |
| 124. C2×C7 | C3×#124 | semidirect |
| 148. C7 | C2×C3×#124 | semidirect |
| 150. C2×C3 | #6499 | direct (N × H) |
| 162. C3 | C2×#6499 | direct (N × H) |
| 164. C2 | C3×#6499 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×D4 | 2 |
| C22×C3×Dic14 | 2 |
| C2×C3×C22⋊Dic7 | 2 |
| C3×#6499 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C2×#6499 | 3 |
| C2×C3×#124 | 7 |