Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
492 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 140 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. #10621359 | C2 | semidirect |
| 2. C42×D3×C7 | C2 | semidirect |
| 3. C3×#6439 | C2 | semidirect |
| 5. D3×Dic7⋊C4 | C2 | semidirect |
| 6. #10620942 | C2 | semidirect |
| 7. #10620925 | C2 | semidirect |
| 12. C3×C42×C7 | C22 | semidirect |
| 14. #66629 | C22 | semidirect |
| 15. C4×C7×Dic3 | C22 | semidirect |
| 17. C3×Dic7⋊C4 | C22 | semidirect |
| 18. #66577 | C22 | semidirect |
| 19. Dic7⋊Dic3 | C22 | semidirect |
| 28. #6439 | D3 | direct (N × H) |
| 44. C42×C7 | C2×D3 | semidirect |
| 52. Dic7⋊C4 | C2×D3 | semidirect |
| 59. C42×D3 | D7 | semidirect |
| 85. C3×C42 | C2×D7 | semidirect |
| 92. C4×Dic3 | C2×D7 | semidirect |
| 96. D3×C7 | #126 | semidirect |
| 123. C3×C7 | C2×#126 | semidirect |
| 136. C42 | D3×D7 | semidirect |
| 160. C7 | D3×#126 | semidirect |
| 164. D3 | #6439 | direct (N × H) |
| 174. C3 | C2×#6439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621359 | 2 |
| C42×D3×C7 | 2 |
| C3×#6439 | 2 |
| D3×(C2×D7)⋊C4 | 2 |
| D3×Dic7⋊C4 | 2 |
| #10620942 | 2 |
| #10620925 | 2 |
| C2×#6439 | 3 |
| D3×#126 | 7 |