Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
496 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 152 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. #92101 | C2 | semidirect |
| 2. C3×#4150 | C2 | semidirect |
| 3. C5×#948 | C2 | semidirect |
| 4. C2×#6662 | C2 | semidirect |
| 5. #91315 | C2 | semidirect |
| 6. #91313 | C2 | semidirect |
| 7. #91311 | C2 | semidirect |
| 27. #4150 | D3 | semidirect |
| 54. #948 | D5 | semidirect |
| 165. C3×C5 | #578 | semidirect |
| 198. C5 | #5838 | semidirect |
| 206. C3 | #66087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92101 | 2 |
| C3×#4150 | 2 |
| C5×#948 | 2 |
| C2×#6662 | 2 |
| #91315 | 2 |
| #91313 | 2 |
| #91311 | 2 |
| #66087 | 3 |
| #5838 | 5 |