Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 48 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. C3×D7×D8 | C2 | semidirect |
| 2. #10620833 | C2 | semidirect |
| 3. #10620665 | C2 | semidirect |
| 4. C7×#827 | C2 | semidirect |
| 5. #10620475 | C2 | semidirect |
| 6. #10620473 | C2 | semidirect |
| 7. #10620469 | C2 | semidirect |
| 12. D168 | C22 | semidirect |
| 13. C7×Dic12 | C22 | semidirect |
| 18. C3⋊(C7⋊C16) | C22 | semidirect |
| 19. C7×C3⋊C16 | C22 | semidirect |
| 21. D7×D8 | D3 | semidirect |
| 53. #827 | D7 | semidirect |
| 83. Dic12 | C2×D7 | semidirect |
| 87. C3⋊C16 | C2×D7 | semidirect |
| 119. C3×C7 | #509 | semidirect |
| 155. C7 | #5147 | semidirect |
| 169. C3 | #89686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D7×D8 | 2 |
| #10620833 | 2 |
| #10620665 | 2 |
| C7×#827 | 2 |
| #10620475 | 2 |
| #10620473 | 2 |
| #10620469 | 2 |
| #89686 | 3 |
| #5147 | 7 |