Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
532 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 532 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. C2×C7×#235 | C2 | semidirect |
| 3. C22×C3×C7⋊C8 | C2 | semidirect |
| 4. C2×#66571 | C2 | semidirect |
| 5. C2×#66568 | C2 | semidirect |
| 6. C2×#66567 | C2 | semidirect |
| 7. #10620865 | C2 | direct (N × H) |
| 8. C2×#66562 | C2 | semidirect |
| 13. #66728 | C22 | semidirect |
| 19. C7×#235 | C22 | semidirect |
| 25. C2×C3×C7⋊C8 | C22 | semidirect |
| 26. #66571 | C22 | semidirect |
| 27. #66568 | C22 | semidirect |
| 28. #66567 | C22 | semidirect |
| 29. #66562 | C22 | semidirect |
| 37. C22×C7⋊C8 | D3 | semidirect |
| 81. C2×C7⋊C8 | C2×D3 | semidirect |
| 83. C2×#235 | D7 | semidirect |
| 132. #235 | C2×D7 | semidirect |
| 147. C2×C3×C7 | #135 | semidirect |
| 194. C3×C7 | C2×#135 | semidirect |
| 217. C2×C7 | #904 | semidirect |
| 255. C7 | C2×#904 | semidirect |
| 257. C2×C3 | #6513 | semidirect |
| 273. C3 | C2×#6513 | semidirect |
| 277. C2 | #10620865 | 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 |
| C2×C7×#235 | 2 |
| C22×C3×C7⋊C8 | 2 |
| C2×#66571 | 2 |
| C2×#66568 | 2 |
| C2×#66567 | 2 |
| #10620865 | 2 |
| C2×#66562 | 2 |
| C2×#6513 | 3 |
| C2×#904 | 7 |