Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 68 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. C2×C3×#704 | C2 | semidirect |
| 2. C2×#6738 | C2 | semidirect |
| 4. #91241 | C2 | semidirect |
| 5. Dic3⋊#170 | C2 | semidirect |
| 6. #91171 | C2 | semidirect |
| 7. #91169 | C2 | semidirect |
| 23. C2×#704 | D3 | semidirect |
| 45. C3×#170 | D4 | semidirect |
| 73. C2×D15 | M16 | semidirect |
| 108. #170 | #67 | semidirect |
| 163. C3×C5 | #435 | semidirect |
| 203. C5 | #5127 | semidirect |
| 217. C3 | #65694 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#704 | 2 |
| C2×#6738 | 2 |
| #91552 | 2 |
| #91241 | 2 |
| Dic3⋊#170 | 2 |
| #91171 | 2 |
| #91169 | 2 |
| #65694 | 3 |
| #5127 | 5 |