Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 47 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. #10621402 | C2 | semidirect |
| 2. D8×D21 | C2 | semidirect |
| 3. C3×C7×SD32 | C2 | semidirect |
| 4. #10620667 | C2 | semidirect |
| 5. #10620665 | C2 | semidirect |
| 6. D336 | C2 | semidirect |
| 7. #10620637 | C2 | semidirect |
| 11. C3×C7×Q16 | C22 | semidirect |
| 16. D168 | C22 | semidirect |
| 18. C3×C7×C16 | C22 | semidirect |
| 19. C3⋊(C7⋊C16) | C22 | semidirect |
| 22. C7×SD32 | D3 | semidirect |
| 41. C7×Q16 | C2×D3 | semidirect |
| 48. C7×C16 | C2×D3 | semidirect |
| 52. C3×SD32 | D7 | semidirect |
| 79. C3×Q16 | C2×D7 | semidirect |
| 86. C3×C16 | C2×D7 | semidirect |
| 96. SD32 | D21 | semidirect |
| 119. C3×C7 | #509 | semidirect |
| 122. Q16 | C2×D21 | semidirect |
| 130. C16 | C2×D21 | semidirect |
| 155. C7 | #4914 | semidirect |
| 169. C3 | #89686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621402 | 2 |
| D8×D21 | 2 |
| C3×C7×SD32 | 2 |
| #10620667 | 2 |
| #10620665 | 2 |
| D336 | 2 |
| #10620637 | 2 |
| #89686 | 3 |
| #4914 | 7 |