Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
196 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 2. C2×C3×C5×C16 | C2 | semidirect |
| 3. C2×C5×C3⋊C16 | C2 | semidirect |
| 4. C5×D3×C16 | C2 | direct (N × H) |
| 11. C3×C5×C16 | C22 | semidirect |
| 12. C5×C3⋊C16 | C22 | semidirect |
| 13. C2×D3×C16 | C5 | direct (N × H) |
| 17. C2×C5×C16 | D3 | direct (N × H) |
| 27. C2×C3×C16 | C2×C5 | semidirect |
| 28. C2×C3⋊C16 | C2×C5 | semidirect |
| 29. D3×C16 | C2×C5 | direct (N × H) |
| 36. C5×C16 | C2×D3 | direct (N × H) |
| 39. C2×C5×D3 | C16 | direct (N × H) |
| 49. C3×C16 | C22×C5 | semidirect |
| 50. C3⋊C16 | C22×C5 | semidirect |
| 62. C2×C16 | C5×D3 | direct (N × H) |
| 63. C2×C3×C5 | C2×C16 | semidirect |
| 65. C5×D3 | C2×C16 | direct (N × H) |
| 86. C16 | C2×C5×D3 | direct (N × H) |
| 87. C3×C5 | C22×C16 | semidirect |
| 89. C2×D3 | C5×C16 | direct (N × H) |
| 95. C2×C5 | D3×C16 | direct (N × H) |
| 105. C2×C3 | C2×C5×C16 | semidirect |
| 107. D3 | C2×C5×C16 | direct (N × H) |
| 108. C5 | C2×D3×C16 | direct (N × H) |
| 115. C3 | C22×C5×C16 | semidirect |
| 117. C2 | C5×D3×C16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D3×C8 | 2 |
| C2×C3×C5×C16 | 2 |
| C2×C5×C3⋊C16 | 2 |
| C5×D3×C16 | 2 |
| C22×C5×C16 | 3 |
| C2×D3×C16 | 5 |