Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 82 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×#4093 | C2 | semidirect |
| 3. C3×D4×Dic5 | C2 | semidirect |
| 5. C3×#3967 | C2 | semidirect |
| 6. C3×#3953 | C2 | semidirect |
| 7. C3×#3946 | C2 | semidirect |
| 8. #65454 | C3 | direct (N × H) |
| 23. C2×C5×SD16 | C2×C3 | semidirect |
| 24. #4093 | C2×C3 | semidirect |
| 25. D4×Dic5 | C2×C3 | semidirect |
| 27. #3967 | C2×C3 | semidirect |
| 28. #3953 | C2×C3 | semidirect |
| 29. #3946 | C2×C3 | semidirect |
| 46. C2×C3×SD16 | D5 | semidirect |
| 109. C2×SD16 | C3×D5 | semidirect |
| 163. C3×C5 | #463 | semidirect |
| 203. C5 | C3×#463 | semidirect |
| 217. C3 | #65454 | 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×#4093 | 2 |
| C3×D4×Dic5 | 2 |
| C2×C3×#686 | 2 |
| C3×#3967 | 2 |
| C3×#3953 | 2 |
| C3×#3946 | 2 |
| #65454 | 3 |
| C3×#463 | 5 |