Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 2. #91469 | C2 | semidirect |
| 5. #90986 | C2 | semidirect |
| 6. #90985 | C2 | semidirect |
| 7. Dic3⋊#168 | C2 | semidirect |
| 30. C3×C5×D4 | Q8 | semidirect |
| 84. C5×D4 | Dic6 | semidirect |
| 108. C3×D4 | Dic10 | semidirect |
| 141. C3×C5 | #476 | semidirect |
| 160. D4 | #1204 | semidirect |
| 174. C5 | #4761 | semidirect |
| 186. C3 | #65297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×Dic3 | 2 |
| #91469 | 2 |
| #91116 | 2 |
| C3×#3964 | 2 |
| #90986 | 2 |
| #90985 | 2 |
| Dic3⋊#168 | 2 |
| #65297 | 3 |
| #4761 | 5 |