Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
164 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 164 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 |
|---|---|---|
| 3. C3×#3961 | C2 | direct (N × H) |
| 5. C2×#3961 | C3 | direct (N × H) |
| 17. #3961 | C2×C3 | direct (N × H) |
| 67. C2×C3×C5 | Q32 | semidirect |
| 91. C3×C5 | C2×Q32 | semidirect |
| 97. C2×C5 | C3×Q32 | semidirect |
| 108. C2×C3 | #3961 | direct (N × H) |
| 110. C5 | C2×C3×Q32 | semidirect |
| 116. C3 | C2×#3961 | direct (N × H) |
| 117. C2 | C3×#3961 | 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×Q16 | 2 |
| C2×C3×Dic20 | 2 |
| C3×#3961 | 2 |
| C2×C3×#672 | 2 |
| C2×#3961 | 3 |
| C2×C3×Q32 | 5 |