Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
220 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 6. #65162 | C3 | direct (N × H) |
| 14. C3×Dic20 | C4 | semidirect |
| 42. Dic20 | C3×C4 | semidirect |
| 50. C3×Dic5 | Q16 | semidirect |
| 91. Dic5 | C3×Q16 | semidirect |
| 100. C3×C5 | C4×Q16 | semidirect |
| 123. C5 | C3×C4×Q16 | semidirect |
| 131. C3 | #65162 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic20 | 2 |
| C3×#4033 | 2 |
| C3×C5×#107 | 2 |
| C3×C8×Dic5 | 2 |
| C3×#3942 | 2 |
| #65162 | 3 |
| C3×C4×Q16 | 5 |