Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
280 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 280 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. C3×#4086 | C2 | semidirect |
| 2. C2×C3×#686 | C2 | semidirect |
| 3. C2×C3×D40 | C2 | semidirect |
| 4. C3×#4039 | C2 | semidirect |
| 5. C3×C5×#102 | C2 | semidirect |
| 6. C3×#3946 | C2 | semidirect |
| 7. C3×#3941 | C2 | semidirect |
| 8. #65075 | C3 | direct (N × H) |
| 23. #4086 | C2×C3 | semidirect |
| 24. C2×#686 | C2×C3 | semidirect |
| 25. C2×D40 | C2×C3 | semidirect |
| 26. #4039 | C2×C3 | semidirect |
| 27. C5×#102 | C2×C3 | semidirect |
| 28. #3946 | C2×C3 | semidirect |
| 29. #3941 | C2×C3 | semidirect |
| 44. C3×D20 | D4 | semidirect |
| 54. C3×#102 | D5 | semidirect |
| 83. C3×Dic5 | D8 | semidirect |
| 111. D20 | C3×D4 | semidirect |
| 121. #102 | C3×D5 | semidirect |
| 160. Dic5 | C3×D8 | semidirect |
| 174. C3×C5 | #459 | semidirect |
| 220. C5 | C3×#459 | semidirect |
| 236. C3 | #65075 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4086 | 2 |
| C2×C3×#686 | 2 |
| C2×C3×D40 | 2 |
| C3×#4039 | 2 |
| C3×C5×#102 | 2 |
| C3×#3946 | 2 |
| C3×#3941 | 2 |
| #65075 | 3 |
| C3×#459 | 5 |