Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
268 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 88 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. C2×#6648 | C2 | semidirect |
| 3. C2×D3×#168 | C2 | semidirect |
| 4. #91104 | C2 | semidirect |
| 5. C5×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C3×C8×Dic5 | C2 | semidirect |
| 7. #90982 | C2 | semidirect |
| 29. C8×Dic5 | D3 | semidirect |
| 41. #1203 | C8 | semidirect |
| 44. C3×#168 | D4 | semidirect |
| 51. (C2×D3)⋊C8 | D5 | semidirect |
| 70. C2×D15 | C2×C8 | semidirect |
| 73. C2×C5×D3 | C2×C8 | semidirect |
| 78. C3×Dic5 | C2×C8 | semidirect |
| 108. #168 | D12 | semidirect |
| 149. Dic5 | D3×C8 | semidirect |
| 163. C3×C5 | C8×D4 | semidirect |
| 170. C2×D3 | C8×D5 | semidirect |
| 203. C5 | C8×D12 | semidirect |
| 217. C3 | #65014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#1203 | 2 |
| C2×#6648 | 2 |
| C2×D3×#168 | 2 |
| #91104 | 2 |
| C5×(C2×D3)⋊C8 | 2 |
| C3×C8×Dic5 | 2 |
| #90982 | 2 |
| #65014 | 3 |
| C8×D12 | 5 |