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. D3×C7×D8 | C2 | semidirect |
| 2. #10620835 | C2 | semidirect |
| 3. #10620666 | C2 | semidirect |
| 4. C3×#6400 | C2 | semidirect |
| 5. #10620479 | C2 | semidirect |
| 6. #10620472 | C2 | semidirect |
| 7. #10620470 | C2 | semidirect |
| 12. Dic84 | C22 | semidirect |
| 16. C3×D56 | C22 | semidirect |
| 18. C3⋊(C7⋊C16) | C22 | semidirect |
| 19. C3×C7⋊C16 | C22 | semidirect |
| 25. #6400 | D3 | semidirect |
| 46. D56 | C2×D3 | semidirect |
| 49. C7⋊C16 | C2×D3 | semidirect |
| 51. D3×D8 | D7 | semidirect |
| 119. C3×C7 | #509 | semidirect |
| 155. C7 | #4911 | semidirect |
| 169. C3 | #89919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C7×D8 | 2 |
| #10620835 | 2 |
| #10620666 | 2 |
| C3×#6400 | 2 |
| #10620479 | 2 |
| #10620472 | 2 |
| #10620470 | 2 |
| #89919 | 3 |
| #4911 | 7 |