Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 3. C3×#4004 | C2 | semidirect |
| 4. C3×#4002 | C2 | semidirect |
| 5. #65757 | C3 | direct (N × H) |
| 17. #4004 | C2×C3 | semidirect |
| 18. #4002 | C2×C3 | semidirect |
| 109. C3×C5 | #432 | semidirect |
| 139. C5 | C3×#432 | semidirect |
| 150. C3 | #65757 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×Dic5 | 2 |
| C3×C22⋊#170 | 2 |
| C3×#4004 | 2 |
| C3×#4002 | 2 |
| #65757 | 3 |
| C3×#432 | 5 |