Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
596 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 1. C2×#66728 | C2 | semidirect |
| 2. C22×C3×D28 | C2 | semidirect |
| 3. C2×C7×#208 | C2 | semidirect |
| 4. #10620874 | C2 | direct (N × H) |
| 5. C2×#66565 | C2 | semidirect |
| 6. C2×#66561 | C2 | semidirect |
| 12. #66728 | C22 | semidirect |
| 13. C2×D84 | C22 | semidirect |
| 15. C2×Dic42 | C22 | semidirect |
| 19. C2×C3×D28 | C22 | semidirect |
| 20. C7×#208 | C22 | semidirect |
| 21. C2×C7×C3⋊C8 | C22 | semidirect |
| 22. #66565 | C22 | semidirect |
| 23. #66561 | C22 | semidirect |
| 25. C22×D28 | D3 | semidirect |
| 43. D84 | C23 | semidirect |
| 46. Dic42 | C23 | semidirect |
| 50. C7×C3⋊C8 | C23 | semidirect |
| 60. C2×D28 | C2×D3 | semidirect |
| 72. C2×#208 | D7 | semidirect |
| 120. #208 | C2×D7 | semidirect |
| 121. C2×C3⋊C8 | C2×D7 | semidirect |
| 123. C2×C3×C7 | AGL(1,ℤ/8) | semidirect |
| 164. C3⋊C8 | C22×D7 | semidirect |
| 165. C3×C7 | C2×AGL(1,ℤ/8) | semidirect |
| 183. C2×C7 | #932 | semidirect |
| 219. C7 | C2×#932 | semidirect |
| 222. C2×C3 | #6471 | semidirect |
| 237. C3 | C2×#6471 | semidirect |
| 241. C2 | #10620874 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C22×C3×D28 | 2 |
| C2×C7×#208 | 2 |
| #10620874 | 2 |
| C2×#66565 | 2 |
| C2×#66561 | 2 |
| C2×#6471 | 3 |
| C2×#932 | 7 |