Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
880 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 298 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. C22×C3×C5×D8 | C2 | semidirect |
| 2. C22×C5×D24 | C2 | semidirect |
| 3. C2×C5×#826 | C2 | direct (N × H) |
| 4. C22×C5×C3⋊C16 | C2 | semidirect |
| 9. C2×C3×C5×D8 | C22 | semidirect |
| 12. C2×C5×D24 | C22 | semidirect |
| 13. C5×#826 | C22 | direct (N × H) |
| 14. C2×C5×C3⋊C16 | C22 | semidirect |
| 15. C22×#826 | C5 | direct (N × H) |
| 17. C22×C5×D8 | D3 | semidirect |
| 28. C3×C5×D8 | C23 | semidirect |
| 32. C5×D24 | C23 | semidirect |
| 33. C5×C3⋊C16 | C23 | semidirect |
| 34. C22×C3×D8 | C2×C5 | semidirect |
| 35. C22×D24 | C2×C5 | semidirect |
| 36. C2×#826 | C2×C5 | direct (N × H) |
| 37. C22×C3⋊C16 | C2×C5 | semidirect |
| 43. C2×C5×D8 | C2×D3 | semidirect |
| 64. C2×C3×D8 | C22×C5 | semidirect |
| 67. C2×D24 | C22×C5 | semidirect |
| 68. #826 | C22×C5 | direct (N × H) |
| 69. C2×C3⋊C16 | C22×C5 | semidirect |
| 80. C5×D8 | C22×D3 | semidirect |
| 85. C22×D8 | C5×D3 | semidirect |
| 90. C22×C3×C5 | D16 | semidirect |
| 104. C3×D8 | C23×C5 | semidirect |
| 108. D24 | C23×C5 | semidirect |
| 109. C3⋊C16 | C23×C5 | semidirect |
| 128. C2×D8 | C2×C5×D3 | semidirect |
| 133. C2×C3×C5 | C2×D16 | semidirect |
| 153. C22×C5 | #826 | direct (N × H) |
| 167. D8 | C22×C5×D3 | semidirect |
| 171. C3×C5 | C22×D16 | semidirect |
| 174. C22×C3 | C5×D16 | semidirect |
| 182. C2×C5 | C2×#826 | direct (N × H) |
| 198. C2×C3 | C2×C5×D16 | semidirect |
| 201. C5 | C22×#826 | direct (N × H) |
| 206. C22 | C5×#826 | direct (N × H) |
| 210. C3 | C22×C5×D16 | semidirect |
| 213. C2 | C2×C5×#826 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×D8 | 2 |
| C22×C5×D24 | 2 |
| C2×C5×#826 | 2 |
| C22×C5×C3⋊C16 | 2 |
| C22×C5×D16 | 3 |
| C22×#826 | 5 |