Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
326 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 94 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×C32×C7×D4 | C2 | semidirect |
| 2. C3×#66728 | C2 | semidirect |
| 3. C3×#66633 | C2 | semidirect |
| 4. C3×#66632 | C2 | semidirect |
| 5. C3×#66627 | C2 | semidirect |
| 6. #10621415 | C3 | direct (N × H) |
| 13. C3×D84 | C22 | semidirect |
| 15. C3×Dic42 | C22 | semidirect |
| 16. C3×C3⋊(C7⋊C8) | C22 | semidirect |
| 18. C2×C3×C7×D4 | D3 | semidirect |
| 19. C2×C3×C7×D4 | C2×C3 | semidirect |
| 20. #66728 | C2×C3 | semidirect |
| 22. #66633 | C2×C3 | semidirect |
| 23. #66632 | C2×C3 | semidirect |
| 24. #66627 | C2×C3 | semidirect |
| 52. D84 | C22×C3 | semidirect |
| 54. Dic42 | C22×C3 | semidirect |
| 59. C3⋊(C7⋊C8) | C22×C3 | semidirect |
| 61. C2×C32×D4 | D7 | semidirect |
| 70. C2×C7×D4 | C3×D3 | semidirect |
| 107. C32×C7 | AGL(1,ℤ/8) | semidirect |
| 119. C2×C3×D4 | C3×D7 | semidirect |
| 120. C2×C3×D4 | D21 | semidirect |
| 181. C3×C7 | #932 | semidirect |
| 182. C3×C7 | C3×AGL(1,ℤ/8) | semidirect |
| 188. C2×D4 | C3×D21 | semidirect |
| 217. C32 | #6495 | semidirect |
| 227. C7 | C3×#932 | semidirect |
| 249. C3 | C3×#6495 | semidirect |
| 250. C3 | #10621415 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C7×D4 | 2 |
| C3×#66728 | 2 |
| C3×#66633 | 2 |
| C3×#66632 | 2 |
| C3×#66627 | 2 |
| #10621415 | 3 |
| C3×#6495 | 3 |
| C3×#932 | 7 |