Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 180 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×Dic20 | C2 | semidirect |
| 3. C3×#3959 | C2 | direct (N × H) |
| 4. C2×C3×#672 | C2 | semidirect |
| 5. C2×#3959 | C3 | direct (N × H) |
| 12. C3×Dic20 | C22 | semidirect |
| 13. C3×#672 | C22 | semidirect |
| 16. C2×Dic20 | C2×C3 | semidirect |
| 17. #3959 | C2×C3 | direct (N × H) |
| 18. C2×#672 | C2×C3 | semidirect |
| 38. Dic20 | C22×C3 | semidirect |
| 39. #672 | C22×C3 | semidirect |
| 69. C2×C3×C5 | SD32 | semidirect |
| 94. C3×C5 | C2×SD32 | semidirect |
| 102. C2×C5 | C3×SD32 | semidirect |
| 114. C2×C3 | #3959 | direct (N × H) |
| 116. C5 | C2×C3×SD32 | semidirect |
| 123. C3 | C2×#3959 | direct (N × H) |
| 125. C2 | C3×#3959 | 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×D8 | 2 |
| C2×C3×Dic20 | 2 |
| C3×#3959 | 2 |
| C2×C3×#672 | 2 |
| C2×#3959 | 3 |
| C2×C3×SD32 | 5 |