Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
| 86. #168 | Dic6 | semidirect |
| 106. C3×C8 | Dic10 | semidirect |
| 127. C3×C5 | #501 | semidirect |
| 149. C8 | #1204 | semidirect |
| 153. C5 | #4702 | semidirect |
| 163. C3 | #65165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91468 | 2 |
| #91388 | 2 |
| #91101 | 2 |
| C5×#818 | 2 |
| C3×#3947 | 2 |
| #90988 | 2 |
| #90985 | 2 |
| #65165 | 3 |
| #4702 | 5 |