Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
358 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 80 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×D4×C3⋊D3 | C2 | semidirect |
| 2. C7×#3802 | C2 | semidirect |
| 3. C3×C7×#213 | C2 | semidirect |
| 4. C7×#3714 | C2 | semidirect |
| 5. C7×#3710 | C2 | semidirect |
| 9. C32×C7×D4 | C22 | semidirect |
| 11. C7×C4⋊(C3⋊D3) | C22 | semidirect |
| 13. C3×C7×D12 | C22 | semidirect |
| 15. C3×C7×C3⋊C8 | C22 | semidirect |
| 21. C7×#213 | D3 | semidirect |
| 24. #63926 | C7 | direct (N × H) |
| 40. C3×C7×D4 | C2×D3 | semidirect |
| 47. C7×D12 | C2×D3 | semidirect |
| 51. C7×C3⋊C8 | C2×D3 | semidirect |
| 52. D4×C3⋊D3 | C2×C7 | semidirect |
| 53. #3802 | C2×C7 | semidirect |
| 54. C3×#213 | C2×C7 | semidirect |
| 55. #3714 | C2×C7 | semidirect |
| 56. #3710 | C2×C7 | semidirect |
| 60. C7×C3⋊D3 | D8 | semidirect |
| 88. C32×D4 | C22×C7 | semidirect |
| 90. C4⋊(C3⋊D3) | C22×C7 | semidirect |
| 92. C3×D12 | C22×C7 | semidirect |
| 94. C3×C3⋊C8 | C22×C7 | semidirect |
| 95. C32×C7 | C2×D8 | semidirect |
| 102. C7×D4 | D32 | semidirect |
| 110. #213 | D3×C7 | semidirect |
| 148. C3×D4 | C2×D3×C7 | semidirect |
| 155. D12 | C2×D3×C7 | semidirect |
| 159. C3⋊C8 | C2×D3×C7 | semidirect |
| 161. C3×C7 | D3×D8 | semidirect |
| 165. C3⋊D3 | C7×D8 | semidirect |
| 195. C32 | C2×C7×D8 | semidirect |
| 202. D4 | D32×C7 | semidirect |
| 205. C7 | #63926 | direct (N × H) |
| 227. C3 | D3×C7×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D4×C3⋊D3 | 2 |
| C7×#3802 | 2 |
| C3×C7×#213 | 2 |
| C7×#3714 | 2 |
| C7×#3710 | 2 |
| D3×C7×D8 | 3 |
| #63926 | 7 |