Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 372 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. D3×C7×M16 | C2 | semidirect |
| 3. C3×C7×#100 | C2 | semidirect |
| 4. C7×#833 | C2 | semidirect |
| 5. C7×#823 | C2 | semidirect |
| 14. C3×C7×M16 | C22 | semidirect |
| 15. C7×#208 | C22 | semidirect |
| 22. C7×#100 | D3 | direct (N × H) |
| 23. D3×#100 | C7 | direct (N × H) |
| 48. C7×M16 | C2×D3 | semidirect |
| 51. D3×M16 | C2×C7 | semidirect |
| 52. C3×#100 | C2×C7 | semidirect |
| 53. #833 | C2×C7 | semidirect |
| 54. #823 | C2×C7 | semidirect |
| 90. C3×M16 | C22×C7 | semidirect |
| 91. #208 | C22×C7 | semidirect |
| 99. D3×C7 | #100 | direct (N × H) |
| 104. #100 | D3×C7 | direct (N × H) |
| 132. C3×C7 | C2×#100 | semidirect |
| 142. M16 | C2×D3×C7 | semidirect |
| 177. C7 | D3×#100 | direct (N × H) |
| 183. D3 | C7×#100 | direct (N × H) |
| 196. C3 | C2×C7×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×D4 | 2 |
| D3×C7×M16 | 2 |
| C3×C7×#100 | 2 |
| C7×#833 | 2 |
| C7×#823 | 2 |
| C2×C7×#100 | 3 |
| D3×#100 | 7 |