Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 228 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 |
|---|---|---|
| 4. C4⋊(C3⋊#170) | C2 | semidirect |
| 5. C3×#4004 | C2 | semidirect |
| 6. #91177 | C2 | semidirect |
| 7. Dic3⋊#170 | C2 | semidirect |
| 27. #4004 | D3 | semidirect |
| 149. C3×C5 | #424 | semidirect |
| 182. C5 | #4839 | semidirect |
| 194. C3 | #65708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6740 | 2 |
| C2×#6738 | 2 |
| #91402 | 2 |
| C4⋊(C3⋊#170) | 2 |
| C3×#4004 | 2 |
| #91177 | 2 |
| Dic3⋊#170 | 2 |
| #65708 | 3 |
| #4839 | 5 |