Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 36. C3×C5×C8 | Q8 | semidirect |
| 37. C3⋊#168 | Q8 | semidirect |
| 85. C5×C8 | Dic6 | semidirect |
| 105. C3×C8 | Dic10 | semidirect |
| 127. C3×C5 | #501 | semidirect |
| 149. C8 | #1204 | semidirect |
| 153. C5 | #4876 | semidirect |
| 163. C3 | #65145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91470 | 2 |
| #91384 | 2 |
| #91099 | 2 |
| C5×#817 | 2 |
| C3×#3950 | 2 |
| #90989 | 2 |
| #90986 | 2 |
| #65145 | 3 |
| #4876 | 5 |