Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. #10621384 | C2 | semidirect |
| 3. C3×C4×C7×C8 | C2 | semidirect |
| 4. #10620658 | C2 | semidirect |
| 5. #10620644 | C2 | semidirect |
| 12. Dic84 | C4 | semidirect |
| 13. D168 | C4 | semidirect |
| 14. #66623 | C4 | semidirect |
| 19. C4×C7×C8 | D3 | semidirect |
| 46. C3×C4×C8 | D7 | semidirect |
| 84. C4×C8 | D21 | semidirect |
| 102. C3×C7 | #443 | semidirect |
| 133. C7 | #4700 | semidirect |
| 143. C3 | #89472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621387 | 2 |
| #10621384 | 2 |
| C3×C4×C7×C8 | 2 |
| #10620658 | 2 |
| #10620644 | 2 |
| #89472 | 3 |
| #4700 | 7 |