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. C3×C7×#208 | C2 | semidirect |
| 3. C32×C4×Dic7 | C2 | semidirect |
| 5. #10620516 | C3 | direct (N × H) |
| 8. C3×D84 | C4 | semidirect |
| 10. C3×Dic42 | C4 | semidirect |
| 16. C7×#208 | C2×C3 | semidirect |
| 18. C3×C4×Dic7 | D3 | semidirect |
| 19. C3×C4×Dic7 | C2×C3 | semidirect |
| 32. D84 | C3×C4 | semidirect |
| 34. Dic42 | C3×C4 | semidirect |
| 47. C3×#208 | D7 | semidirect |
| 53. C4×Dic7 | C3×D3 | semidirect |
| 80. C32×C7 | #104 | semidirect |
| 94. #208 | C3×D7 | semidirect |
| 135. C3×C7 | #805 | semidirect |
| 136. C3×C7 | C3×#104 | semidirect |
| 163. C32 | #6399 | semidirect |
| 171. C7 | C3×#805 | semidirect |
| 188. C3 | #10620516 | direct (N × H) |
| 189. C3 | C3×#6399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66728 | 2 |
| C3×C7×#208 | 2 |
| C32×C4×Dic7 | 2 |
| C3×#6399 | 3 |
| #10620516 | 3 |
| C3×#805 | 7 |