Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
208 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 208 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 |
|---|---|---|
| 1. C2×C3×C5×SD16 | C2 | semidirect |
| 2. C3×#4088 | C2 | semidirect |
| 4. C3×#4047 | C2 | semidirect |
| 5. C3×#3968 | C2 | semidirect |
| 6. C3×#3965 | C2 | semidirect |
| 7. C3×#3951 | C2 | semidirect |
| 8. #65466 | C3 | direct (N × H) |
| 25. C2×C5×SD16 | C2×C3 | semidirect |
| 26. #4088 | C2×C3 | semidirect |
| 28. #4047 | C2×C3 | semidirect |
| 29. #3968 | C2×C3 | semidirect |
| 30. #3965 | C2×C3 | semidirect |
| 31. #3951 | C2×C3 | semidirect |
| 50. C2×C3×SD16 | D5 | semidirect |
| 112. C2×SD16 | C3×D5 | semidirect |
| 160. C3×C5 | #471 | semidirect |
| 193. C5 | C3×#471 | semidirect |
| 202. C3 | #65466 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SD16 | 2 |
| C3×#4088 | 2 |
| C3×#4078 | 2 |
| C3×#4047 | 2 |
| C3×#3968 | 2 |
| C3×#3965 | 2 |
| C3×#3951 | 2 |
| #65466 | 3 |
| C3×#471 | 5 |