Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
780 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 202 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. C24×C32×C7 | C2 | semidirect |
| 2. C2×C7×#638 | C2 | semidirect |
| 3. C7×#3757 | C2 | semidirect |
| 7. C22×C7×C3⋊D3 | C22 | semidirect |
| 9. C2×C7×C3⋊Dic3 | C22 | semidirect |
| 10. C24×C3×C7 | D3 | semidirect |
| 13. #64162 | C7 | direct (N × H) |
| 16. C22×C32×C7 | D4 | semidirect |
| 26. C24×C32 | C2×C7 | semidirect |
| 27. C2×#638 | C2×C7 | semidirect |
| 28. #3757 | C2×C7 | semidirect |
| 32. C24×C7 | C3⋊D3 | semidirect |
| 38. C22×C3×C7 | #67 | semidirect |
| 44. C22×C3⋊D3 | C22×C7 | semidirect |
| 46. C2×C3⋊Dic3 | C22×C7 | semidirect |
| 47. C32×C7 | #120 | semidirect |
| 53. C24×C3 | D3×C7 | semidirect |
| 61. C22×C32 | C7×D4 | semidirect |
| 69. C22×C7 | #638 | semidirect |
| 77. C3×C7 | #953 | semidirect |
| 81. C24 | C7×C3⋊D3 | semidirect |
| 89. C22×C3 | C7×#67 | semidirect |
| 93. C32 | C7×#120 | semidirect |
| 99. C7 | #64162 | direct (N × H) |
| 106. C22 | C7×#638 | semidirect |
| 109. C3 | C7×#953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C32×C7 | 2 |
| C2×C7×#638 | 2 |
| C7×#3757 | 2 |
| C7×#953 | 3 |
| #64162 | 7 |