Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 106 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. C3×C7×M32 | C2 | semidirect |
| 3. C7×#812 | C2 | semidirect |
| 4. C7×#798 | C2 | semidirect |
| 5. D3×C7×C16 | C2 | semidirect |
| 14. C3×C7×C16 | C22 | semidirect |
| 15. C7×C3⋊C16 | C22 | semidirect |
| 19. C7×M32 | D3 | direct (N × H) |
| 21. D3×M32 | C7 | direct (N × H) |
| 41. C7×C16 | C2×D3 | semidirect |
| 43. C3×M32 | C2×C7 | semidirect |
| 44. #812 | C2×C7 | semidirect |
| 45. #798 | C2×C7 | semidirect |
| 46. D3×C16 | C2×C7 | semidirect |
| 74. C3×C16 | C22×C7 | semidirect |
| 75. C3⋊C16 | C22×C7 | semidirect |
| 79. D3×C7 | M32 | direct (N × H) |
| 83. M32 | D3×C7 | direct (N × H) |
| 104. C3×C7 | C2×M32 | semidirect |
| 113. C16 | C2×D3×C7 | semidirect |
| 137. C7 | D3×M32 | direct (N × H) |
| 141. D3 | C7×M32 | direct (N × H) |
| 150. C3 | C2×C7×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×C8 | 2 |
| C3×C7×M32 | 2 |
| C7×#812 | 2 |
| C7×#798 | 2 |
| D3×C7×C16 | 2 |
| C2×C7×M32 | 3 |
| D3×M32 | 7 |