Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
284 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 70 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. #91833 | C2 | semidirect |
| 2. C2×C5×#215 | C2 | semidirect |
| 3. C2×C3×#688 | C2 | semidirect |
| 5. C2×#6659 | C2 | semidirect |
| 6. C2×#6657 | C2 | semidirect |
| 7. #90951 | C2 | semidirect |
| 25. C2×#688 | D3 | semidirect |
| 45. C3×#168 | D4 | semidirect |
| 46. C5×C3⋊C8 | D4 | semidirect |
| 49. C2×#215 | D5 | semidirect |
| 77. Dic15 | SD16 | semidirect |
| 107. #168 | #67 | semidirect |
| 135. C3⋊C8 | C22⋊D5 | semidirect |
| 159. C3×C5 | #492 | semidirect |
| 195. C5 | #5175 | semidirect |
| 206. C3 | #65464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91833 | 2 |
| C2×C5×#215 | 2 |
| C2×C3×#688 | 2 |
| #91463 | 2 |
| C2×#6659 | 2 |
| C2×#6657 | 2 |
| #90951 | 2 |
| #65464 | 3 |
| #5175 | 5 |