Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
662 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 136 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. C2×C7×#624 | C2 | semidirect |
| 3. C3×C7×#217 | C2 | semidirect |
| 4. C7×#3722 | C2 | semidirect |
| 8. C22×C7×C3⋊D3 | C4 | semidirect |
| 11. C2×C3×C7×Dic3 | C22 | semidirect |
| 17. C7×#217 | D3 | semidirect |
| 19. #63974 | C7 | direct (N × H) |
| 21. C22×C32×C7 | C2×C4 | semidirect |
| 26. C2×C7×C3⋊D3 | C2×C4 | semidirect |
| 42. C2×C7×Dic3 | C2×D3 | semidirect |
| 45. C2×#624 | C2×C7 | semidirect |
| 46. C3×#217 | C2×C7 | semidirect |
| 47. #3722 | C2×C7 | semidirect |
| 52. C7×C3⋊D3 | C22⋊C4 | semidirect |
| 63. C22×C3×C7 | C4×D3 | semidirect |
| 81. C22×C3⋊D3 | C4×C7 | semidirect |
| 84. C2×C3×Dic3 | C22×C7 | semidirect |
| 86. C32×C7 | C2×C22⋊C4 | semidirect |
| 98. #217 | D3×C7 | semidirect |
| 113. C22×C32 | C2×C4×C7 | semidirect |
| 118. C2×C3⋊D3 | C2×C4×C7 | semidirect |
| 128. C22×C7 | #624 | semidirect |
| 143. C2×Dic3 | C2×D3×C7 | semidirect |
| 146. C3×C7 | D3×C22⋊C4 | semidirect |
| 151. C3⋊D3 | C7×C22⋊C4 | semidirect |
| 166. C22×C3 | C4×D3×C7 | semidirect |
| 182. C32 | C2×C7×C22⋊C4 | semidirect |
| 190. C7 | #63974 | direct (N × H) |
| 209. C22 | C7×#624 | semidirect |
| 213. C3 | D3×C7×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×C3⋊D3 | 2 |
| C2×C7×#624 | 2 |
| C3×C7×#217 | 2 |
| C7×#3722 | 2 |
| D3×C7×C22⋊C4 | 3 |
| #63974 | 7 |