Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
192 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 74 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×C5×#106 | C2 | semidirect |
| 5. C3×#3948 | C2 | semidirect |
| 6. C3×#3942 | C2 | semidirect |
| 7. C3×#3939 | C2 | semidirect |
| 8. #65156 | C3 | direct (N × H) |
| 23. C5×#106 | C2×C3 | semidirect |
| 25. #3948 | C2×C3 | semidirect |
| 26. #3942 | C2×C3 | semidirect |
| 27. #3939 | C2×C3 | semidirect |
| 44. C3×#106 | D5 | semidirect |
| 98. #106 | C3×D5 | semidirect |
| 141. C3×C5 | #485 | semidirect |
| 174. C5 | C3×#485 | semidirect |
| 186. C3 | #65156 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4043 | 2 |
| C3×#4038 | 2 |
| C3×C5×#106 | 2 |
| C3×#3952 | 2 |
| C3×#3948 | 2 |
| C3×#3942 | 2 |
| C3×#3939 | 2 |
| #65156 | 3 |
| C3×#485 | 5 |