Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 134 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×C3×C7×M16 | C2 | semidirect |
| 3. C2×C7×#208 | C2 | semidirect |
| 4. C7×(C2×D3)⋊C8 | C2 | semidirect |
| 14. C2×C3×C7×C8 | C22 | semidirect |
| 16. C2×C7×C3⋊C8 | C22 | semidirect |
| 19. C2×C7×M16 | D3 | semidirect |
| 21. #5126 | C7 | direct (N × H) |
| 47. C2×C7×C8 | C2×D3 | semidirect |
| 49. C2×C3×M16 | C2×C7 | semidirect |
| 50. C2×#208 | C2×C7 | semidirect |
| 51. (C2×D3)⋊C8 | C2×C7 | semidirect |
| 58. C2×D3×C7 | M16 | semidirect |
| 87. C2×C3×C8 | C22×C7 | semidirect |
| 89. C2×C3⋊C8 | C22×C7 | semidirect |
| 96. C2×M16 | D3×C7 | semidirect |
| 124. C3×C7 | #407 | semidirect |
| 135. C2×C8 | C2×D3×C7 | semidirect |
| 146. C2×D3 | C7×M16 | semidirect |
| 166. C7 | #5126 | direct (N × H) |
| 182. C3 | C7×#407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D3×C7 | 2 |
| C2×C3×C7×M16 | 2 |
| C2×C7×#208 | 2 |
| C7×(C2×D3)⋊C8 | 2 |
| C7×#407 | 3 |
| #5126 | 7 |