Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
3952 conjugacy classes of subgroups; only the 1290 normal subgroups are shown.
This group has 3952 conjugacy classes of subgroups — too many to draw. Only its 1290 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. C23×C5×D12 | C2 | semidirect |
| 2. C23×C3×C5×C8 | C2 | semidirect |
| 3. C22×C5×D24 | C2 | direct (N × H) |
| 8. C22×C5×D12 | C22 | semidirect |
| 9. C22×C3×C5×C8 | C22 | semidirect |
| 10. C2×C5×D24 | C22 | direct (N × H) |
| 11. C23×D24 | C5 | direct (N × H) |
| 14. C23×C5×C8 | D3 | semidirect |
| 21. C2×C5×D12 | C23 | semidirect |
| 22. C2×C3×C5×C8 | C23 | semidirect |
| 23. C5×D24 | C23 | direct (N × H) |
| 24. C23×D12 | C2×C5 | semidirect |
| 25. C23×C3×C8 | C2×C5 | semidirect |
| 26. C22×D24 | C2×C5 | direct (N × H) |
| 32. C22×C5×C8 | C2×D3 | semidirect |
| 34. C23×C3×C5 | D8 | semidirect |
| 41. C5×D12 | C24 | semidirect |
| 42. C3×C5×C8 | C24 | semidirect |
| 46. C22×D12 | C22×C5 | semidirect |
| 47. C22×C3×C8 | C22×C5 | semidirect |
| 48. C2×D24 | C22×C5 | direct (N × H) |
| 57. C2×C5×C8 | C22×D3 | semidirect |
| 60. C23×C8 | C5×D3 | semidirect |
| 61. C22×C3×C5 | C2×D8 | semidirect |
| 73. C2×D12 | C23×C5 | semidirect |
| 74. C2×C3×C8 | C23×C5 | semidirect |
| 75. D24 | C23×C5 | direct (N × H) |
| 78. C23×C5 | D24 | direct (N × H) |
| 84. C5×C8 | C23×D3 | semidirect |
| 90. C22×C8 | C2×C5×D3 | semidirect |
| 91. C2×C3×C5 | C22×D8 | semidirect |
| 94. C23×C3 | C5×D8 | semidirect |
| 101. D12 | C24×C5 | semidirect |
| 102. C3×C8 | C24×C5 | semidirect |
| 105. C22×C5 | C2×D24 | direct (N × H) |
| 117. C2×C8 | C22×C5×D3 | semidirect |
| 118. C3×C5 | C23×D8 | semidirect |
| 119. C22×C3 | C2×C5×D8 | semidirect |
| 126. C2×C5 | C22×D24 | direct (N × H) |
| 130. C23 | C5×D24 | direct (N × H) |
| 136. C8 | C23×C5×D3 | semidirect |
| 137. C2×C3 | C22×C5×D8 | semidirect |
| 140. C5 | C23×D24 | direct (N × H) |
| 143. C22 | C2×C5×D24 | direct (N × H) |
| 147. C3 | C23×C5×D8 | semidirect |
| 149. C2 | C22×C5×D24 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C5×D12 | 2 |
| C23×C3×C5×C8 | 2 |
| C22×C5×D24 | 2 |
| C23×C5×D8 | 3 |
| C23×D24 | 5 |