Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
196 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 94 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. #65163 | C3 | direct (N × H) |
| 26. C3×C5×C8 | Q8 | semidirect |
| 27. C3×#168 | Q8 | semidirect |
| 61. C5×C8 | C3×Q8 | semidirect |
| 62. #168 | C3×Q8 | semidirect |
| 78. C3×C8 | Dic10 | semidirect |
| 93. C3×C5 | #500 | semidirect |
| 111. C8 | C3×Dic10 | semidirect |
| 115. C5 | C3×#500 | semidirect |
| 123. C3 | #65163 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4034 | 2 |
| C3×C5×#107 | 2 |
| C3×#3950 | 2 |
| C3×C8×Dic5 | 2 |
| C3×#3939 | 2 |
| #65163 | 3 |
| C3×#500 | 5 |