Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
256 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 76 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. C4×C5×Dic6 | C2 | semidirect |
| 3. C2×#6660 | C2 | semidirect |
| 4. C3×C4⋊#168 | C2 | semidirect |
| 5. #90969 | C2 | semidirect |
| 22. C4⋊#168 | D3 | semidirect |
| 34. C5×Dic6 | D4 | semidirect |
| 38. C4×Dic6 | D5 | semidirect |
| 57. C3×C4×C5 | SD16 | semidirect |
| 105. Dic6 | D20 | semidirect |
| 114. C4×C5 | #204 | semidirect |
| 127. C3×C5 | #460 | semidirect |
| 133. C3×C4 | #688 | semidirect |
| 159. C5 | #4848 | semidirect |
| 167. C4 | #6660 | semidirect |
| 170. C3 | #65316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91763 | 2 |
| C4×C5×Dic6 | 2 |
| C2×#6660 | 2 |
| C3×C4⋊#168 | 2 |
| #90969 | 2 |
| #65316 | 3 |
| #4848 | 5 |