Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. C3×#4150 | C2 | semidirect |
| 2. C3×C5×AGL(1,ℤ/8) | C2 | semidirect |
| 3. C3×#4082 | C2 | semidirect |
| 4. C3×#4078 | C2 | semidirect |
| 5. C3×#3969 | C2 | semidirect |
| 6. C3×#3957 | C2 | semidirect |
| 7. C3×#3956 | C2 | semidirect |
| 8. #65490 | C3 | direct (N × H) |
| 27. #4150 | C2×C3 | semidirect |
| 28. C5×AGL(1,ℤ/8) | C2×C3 | semidirect |
| 29. #4082 | C2×C3 | semidirect |
| 30. #4078 | C2×C3 | semidirect |
| 31. #3969 | C2×C3 | semidirect |
| 32. #3957 | C2×C3 | semidirect |
| 33. #3956 | C2×C3 | semidirect |
| 58. C3×AGL(1,ℤ/8) | D5 | semidirect |
| 133. AGL(1,ℤ/8) | C3×D5 | semidirect |
| 193. C3×C5 | #454 | semidirect |
| 237. C5 | C3×#454 | semidirect |
| 249. C3 | #65490 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4150 | 2 |
| C3×C5×AGL(1,ℤ/8) | 2 |
| C3×#4082 | 2 |
| C3×#4078 | 2 |
| C3×#3969 | 2 |
| C3×#3957 | 2 |
| C3×#3956 | 2 |
| #65490 | 3 |
| C3×#454 | 5 |