Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
212 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 64 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. #10621390 | C2 | semidirect |
| 3. #10620850 | C2 | semidirect |
| 4. C7×#825 | C2 | semidirect |
| 5. C3×#6396 | C2 | semidirect |
| 6. #10620515 | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 18. #66571 | C4 | semidirect |
| 19. #66568 | C4 | semidirect |
| 20. #66567 | C4 | semidirect |
| 21. #66562 | C4 | semidirect |
| 28. #6396 | D3 | semidirect |
| 68. #825 | D7 | semidirect |
| 145. C3×C7 | #443 | semidirect |
| 189. C7 | #4895 | semidirect |
| 202. C3 | #89596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621390 | 2 |
| #10620865 | 2 |
| #10620850 | 2 |
| C7×#825 | 2 |
| C3×#6396 | 2 |
| #10620515 | 2 |
| Dic3×C7⋊C8 | 2 |
| #89596 | 3 |
| #4895 | 7 |