Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
324 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 66 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×#6765 | C2 | semidirect |
| 2. C2×#6706 | C2 | semidirect |
| 3. #91460 | C2 | semidirect |
| 4. C2×#6653 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C3×#3953 | C2 | semidirect |
| 7. #90974 | C2 | semidirect |
| 30. #3953 | D3 | semidirect |
| 40. Dic30 | D4 | semidirect |
| 46. C3×D20 | D4 | semidirect |
| 57. (C2×D3)⋊C8 | D5 | semidirect |
| 119. D20 | D12 | semidirect |
| 188. C3×C5 | #449 | semidirect |
| 236. C5 | #4781 | semidirect |
| 252. C3 | #65023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6765 | 2 |
| C2×#6706 | 2 |
| #91460 | 2 |
| C2×#6653 | 2 |
| C5×(C2×D3)⋊C8 | 2 |
| C3×#3953 | 2 |
| #90974 | 2 |
| #65023 | 3 |
| #4781 | 5 |