Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 2. C2×C3×#687 | C2 | semidirect |
| 3. C2×C3×#676 | C2 | semidirect |
| 4. C3×#4043 | C2 | semidirect |
| 5. C3×C5×#102 | C2 | semidirect |
| 6. C3×#3948 | C2 | semidirect |
| 7. C3×#3939 | C2 | semidirect |
| 8. #65069 | C3 | direct (N × H) |
| 24. C2×#687 | C2×C3 | semidirect |
| 25. C2×#676 | C2×C3 | semidirect |
| 26. #4043 | C2×C3 | semidirect |
| 27. C5×#102 | C2×C3 | semidirect |
| 28. #3948 | C2×C3 | semidirect |
| 29. #3939 | C2×C3 | semidirect |
| 45. C3×#168 | D4 | semidirect |
| 52. C3×#102 | D5 | semidirect |
| 108. #168 | C3×D4 | semidirect |
| 115. #102 | C3×D5 | semidirect |
| 163. C3×C5 | #468 | semidirect |
| 203. C5 | C3×#468 | semidirect |
| 217. C3 | #65069 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4084 | 2 |
| C2×C3×#687 | 2 |
| C2×C3×#676 | 2 |
| C3×#4043 | 2 |
| C3×C5×#102 | 2 |
| C3×#3948 | 2 |
| C3×#3939 | 2 |
| #65069 | 3 |
| C3×#468 | 5 |