Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
472 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 198 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. C3×#4082 | C2 | semidirect |
| 3. C3×#4081 | C2 | semidirect |
| 4. C3×D4×Dic5 | C2 | semidirect |
| 5. C3×C4×Dic10 | C2 | semidirect |
| 6. #66047 | C3 | direct (N × H) |
| 19. #4082 | C2×C3 | semidirect |
| 20. #4081 | C2×C3 | semidirect |
| 21. D4×Dic5 | C2×C3 | semidirect |
| 22. C4×Dic10 | C2×C3 | semidirect |
| 108. C3×C5 | #559 | semidirect |
| 131. C5 | C3×#559 | semidirect |
| 139. C3 | #66047 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#127 | 2 |
| C3×#4082 | 2 |
| C3×#4081 | 2 |
| C3×D4×Dic5 | 2 |
| C3×C4×Dic10 | 2 |
| #66047 | 3 |
| C3×#559 | 5 |