Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. C3×C4×C7×C8 | C2 | semidirect |
| 5. #10620654 | C2 | semidirect |
| 6. C8×Dic21 | C2 | semidirect |
| 7. #10620642 | C2 | semidirect |
| 18. #66622 | C4 | semidirect |
| 19. C8×D21 | C4 | semidirect |
| 23. C4×C7×C8 | D3 | semidirect |
| 53. C3×C4×C8 | D7 | semidirect |
| 97. C4×C8 | D21 | semidirect |
| 117. C3×C7 | #405 | semidirect |
| 151. C7 | #4689 | semidirect |
| 163. C3 | #89461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66622 | 2 |
| C2×C8×D21 | 2 |
| #10621355 | 2 |
| C3×C4×C7×C8 | 2 |
| #10620654 | 2 |
| C8×Dic21 | 2 |
| #10620642 | 2 |
| #89461 | 3 |
| #4689 | 7 |