Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C7×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C3×#66728 | C2 | semidirect |
| 3. C3×#66627 | C2 | semidirect |
| 4. #11759220 | C2 | semidirect |
| 5. #11759217 | C2 | semidirect |
| 13. C3×D84 | C22 | semidirect |
| 15. C3×Dic42 | C22 | semidirect |
| 16. C3×C3⋊(C7⋊C8) | C22 | semidirect |
| 17. #66728 | D3 | semidirect |
| 22. #66627 | D3 | semidirect |
| 45. D84 | C2×D3 | semidirect |
| 47. Dic42 | C2×D3 | semidirect |
| 59. C3⋊(C7⋊C8) | C2×D3 | semidirect |
| 61. C2×C4⋊(C3⋊D3) | D7 | semidirect |
| 107. C32×C7 | AGL(1,ℤ/8) | semidirect |
| 181. C3×C7 | #908 | semidirect |
| 182. C3×C7 | #949 | semidirect |
| 217. C32 | #6495 | semidirect |
| 227. C7 | #63825 | semidirect |
| 249. C3 | #10620861 | semidirect |
| 250. C3 | #10620866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C4⋊(C3⋊D3) | 2 |
| C3×#66728 | 2 |
| C3×#66627 | 2 |
| #11759220 | 2 |
| #11759217 | 2 |
| #10620866 | 3 |
| #10620861 | 3 |
| #63825 | 7 |