Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
248 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 1. C2×#6706 | C2 | semidirect |
| 2. C2×C5×D3×C8 | C2 | semidirect |
| 4. #91365 | C2 | semidirect |
| 5. C3×#3949 | C2 | semidirect |
| 6. #90974 | C2 | semidirect |
| 7. #90968 | C2 | semidirect |
| 28. #3949 | D3 | semidirect |
| 44. C3×C5×C8 | D4 | semidirect |
| 47. C2×D3×C8 | D5 | semidirect |
| 73. C2×C5×D3 | SD16 | semidirect |
| 108. C5×C8 | D12 | semidirect |
| 135. C3×C8 | C22⋊D5 | semidirect |
| 163. C3×C5 | #465 | semidirect |
| 170. C2×D3 | #677 | semidirect |
| 197. C8 | #1203 | semidirect |
| 203. C5 | #4864 | semidirect |
| 217. C3 | #65403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6706 | 2 |
| C2×C5×D3×C8 | 2 |
| #91460 | 2 |
| #91365 | 2 |
| C3×#3949 | 2 |
| #90974 | 2 |
| #90968 | 2 |
| #65403 | 3 |
| #4864 | 5 |