Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 2. C2×C3×#687 | C2 | semidirect |
| 3. C3×#4070 | C2 | semidirect |
| 4. C2×C3×#681 | C2 | semidirect |
| 5. C3×#3964 | C2 | semidirect |
| 6. C3×#3942 | C2 | semidirect |
| 7. C3×#3939 | C2 | semidirect |
| 8. #65331 | C3 | direct (N × H) |
| 24. C2×#687 | C2×C3 | semidirect |
| 25. #4070 | C2×C3 | semidirect |
| 26. C2×#681 | C2×C3 | semidirect |
| 27. #3964 | C2×C3 | semidirect |
| 28. #3942 | C2×C3 | semidirect |
| 29. #3939 | C2×C3 | semidirect |
| 45. C3×#168 | D4 | semidirect |
| 108. #168 | C3×D4 | semidirect |
| 163. C3×C5 | #468 | semidirect |
| 203. C5 | C3×#468 | semidirect |
| 217. C3 | #65331 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#121 | 2 |
| C2×C3×#687 | 2 |
| C3×#4070 | 2 |
| C2×C3×#681 | 2 |
| C3×#3964 | 2 |
| C3×#3942 | 2 |
| C3×#3939 | 2 |
| #65331 | 3 |
| C3×#468 | 5 |