Finite Group DatabasebetaFinite Group DatabasebetaOrder 4032.
980 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 131 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. #72246811 | C2 | semidirect |
| 2. C3×#10620672 | C2 | semidirect |
| 3. #72245719 | C2 | semidirect |
| 13. C3×#66627 | C22 | semidirect |
| 19. #10620672 | D3 | semidirect |
| 54. #66627 | C2×D3 | semidirect |
| 128. C7×C3⋊D3 | #100 | semidirect |
| 191. C32×C7 | C2×#100 | semidirect |
| 305. C3×C7 | D3×#100 | semidirect |
| 311. C3⋊D3 | #6407 | semidirect |
| 359. C32 | C2×#6407 | semidirect |
| 374. C7 | #10591503 | semidirect |
| 404. C3 | D3×#6407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72246811 | 2 |
| C3×#10620672 | 2 |
| #72245719 | 2 |
| C2×C7×D4×C3⋊D3 | 2 |
| D3×#6407 | 3 |
| #10591503 | 7 |