Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
256 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 1. C2×C3×#677 | C2 | semidirect |
| 3. Dic3×Dic10 | C2 | semidirect |
| 4. C2×#6658 | C2 | semidirect |
| 5. #91105 | C2 | semidirect |
| 6. C5×Dic3⋊C8 | C2 | semidirect |
| 7. #90965 | C2 | semidirect |
| 24. C2×#677 | D3 | semidirect |
| 42. C3×Dic10 | D4 | semidirect |
| 53. Dic3⋊C8 | D5 | semidirect |
| 80. C5×Dic3 | SD16 | semidirect |
| 108. Dic10 | #67 | semidirect |
| 166. C3×C5 | #460 | semidirect |
| 179. Dic3 | #677 | semidirect |
| 207. C5 | #5163 | semidirect |
| 221. C3 | #65137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#677 | 2 |
| #91458 | 2 |
| Dic3×Dic10 | 2 |
| C2×#6658 | 2 |
| #91105 | 2 |
| C5×Dic3⋊C8 | 2 |
| #90965 | 2 |
| #65137 | 3 |
| #5163 | 5 |