Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 8. C4×#689 | C3 | direct (N × H) |
| 15. C3×#689 | C4 | direct (N × H) |
| 55. #689 | C3×C4 | direct (N × H) |
| 66. C3×C4×C5 | Q16 | semidirect |
| 123. C4×C5 | C3×Q16 | semidirect |
| 140. C3×C5 | C4×Q16 | semidirect |
| 147. C3×C4 | #689 | direct (N × H) |
| 169. C5 | C3×C4×Q16 | semidirect |
| 176. C4 | C3×#689 | direct (N × H) |
| 179. C3 | C4×#689 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q8 | 2 |
| C2×C3×#689 | 2 |
| C3×C4×Dic10 | 2 |
| C3×#3967 | 2 |
| C3×#3942 | 2 |
| C3×#3939 | 2 |
| C3×C4×#168 | 2 |
| C4×#689 | 3 |
| C3×C4×Q16 | 5 |