Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
284 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 75 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×C5×SD16 | C2 | semidirect |
| 2. #91833 | C2 | semidirect |
| 3. C2×#6717 | C2 | semidirect |
| 5. C2×#6716 | C2 | semidirect |
| 6. C2×#6706 | C2 | semidirect |
| 7. C8×Dic15 | C2 | semidirect |
| 23. C2×C5×SD16 | D3 | semidirect |
| 45. C3×C5×C8 | D4 | semidirect |
| 46. C3⋊#168 | D4 | semidirect |
| 47. C2×C3×SD16 | D5 | semidirect |
| 77. Dic15 | SD16 | semidirect |
| 106. C5×C8 | #67 | semidirect |
| 111. C2×SD16 | D15 | semidirect |
| 134. C3×C8 | C22⋊D5 | semidirect |
| 159. C3×C5 | #492 | semidirect |
| 190. C8 | #1220 | 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 |
|---|---|
| C2×C3×C5×SD16 | 2 |
| #91833 | 2 |
| C2×#6717 | 2 |
| #91829 | 2 |
| C2×#6716 | 2 |
| C2×#6706 | 2 |
| C8×Dic15 | 2 |
| #65464 | 3 |
| #5175 | 5 |