Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
206 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 64 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. C4×C3⋊Dic21 | C2 | semidirect |
| 3. C3×#66627 | C2 | semidirect |
| 9. C3×C7×D12 | C4 | semidirect |
| 11. C3×C7×Dic6 | C4 | semidirect |
| 18. #66627 | D3 | semidirect |
| 40. C7×D12 | Dic3 | semidirect |
| 42. C7×Dic6 | Dic3 | semidirect |
| 76. C3×D12 | Dic7 | semidirect |
| 78. C3×Dic6 | Dic7 | semidirect |
| 80. C32×C7 | #104 | semidirect |
| 129. D12 | Dic21 | semidirect |
| 131. Dic6 | Dic21 | semidirect |
| 135. C3×C7 | #825 | semidirect |
| 136. C3×C7 | #837 | semidirect |
| 163. C32 | #6411 | semidirect |
| 171. C7 | #63568 | semidirect |
| 188. C3 | #10620513 | semidirect |
| 189. C3 | #10620676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#235 | 2 |
| C4×C3⋊Dic21 | 2 |
| C3×#66627 | 2 |
| #10620676 | 3 |
| #10620513 | 3 |
| #63568 | 7 |