Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 72 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×#6739 | C2 | semidirect |
| 3. C2×D3×#170 | C2 | semidirect |
| 4. #91241 | C2 | semidirect |
| 5. C3×C22⋊#170 | C2 | semidirect |
| 6. #91171 | C2 | semidirect |
| 7. #91171 | C2 | semidirect |
| 29. C22⋊#170 | D3 | semidirect |
| 191. C3×C5 | #408 | semidirect |
| 240. C5 | #4727 | semidirect |
| 256. C3 | #65775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6782 | 2 |
| C2×#6739 | 2 |
| C2×D3×#170 | 2 |
| #91241 | 2 |
| C3×C22⋊#170 | 2 |
| #91171 | 2 |
| #65775 | 3 |
| #4727 | 5 |