Finite Group DatabasebetaFinite Group DatabasebetaOrder 4032.
980 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 148 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. C7×#63559 | C2 | semidirect |
| 2. C3×C7×#833 | C2 | semidirect |
| 3. C7×#63818 | C2 | semidirect |
| 13. C3×C7×#208 | C22 | semidirect |
| 20. C7×#833 | D3 | semidirect |
| 22. #10591503 | C7 | direct (N × H) |
| 55. C7×#208 | C2×D3 | semidirect |
| 59. #63818 | C2×C7 | semidirect |
| 60. C3×#833 | C2×C7 | semidirect |
| 61. #63559 | C2×C7 | semidirect |
| 120. C3×#208 | C22×C7 | semidirect |
| 128. C7×C3⋊D3 | #100 | semidirect |
| 143. #833 | D3×C7 | semidirect |
| 191. C32×C7 | C2×#100 | semidirect |
| 223. #208 | C2×D3×C7 | semidirect |
| 305. C3×C7 | D3×#100 | semidirect |
| 311. C3⋊D3 | C7×#100 | semidirect |
| 359. C32 | C2×C7×#100 | semidirect |
| 374. C7 | #10591503 | direct (N × H) |
| 404. C3 | D3×C7×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#63559 | 2 |
| C3×C7×#833 | 2 |
| C7×#63818 | 2 |
| C2×C7×D4×C3⋊D3 | 2 |
| D3×C7×#100 | 3 |
| #10591503 | 7 |