Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
372 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 107 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×C3×C5×M16 | C2 | semidirect |
| 3. C2×#6710 | C2 | semidirect |
| 4. #91107 | C2 | direct (N × H) |
| 15. C3×C5×M16 | C22 | semidirect |
| 18. #6710 | C22 | semidirect |
| 22. C2×C5×M16 | D3 | semidirect |
| 43. C2×C3×M16 | D5 | semidirect |
| 55. C5×M16 | C2×D3 | semidirect |
| 82. C3×M16 | C2×D5 | semidirect |
| 106. C2×M16 | D15 | semidirect |
| 110. C2×C3×C5 | #100 | semidirect |
| 153. M16 | C2×D15 | semidirect |
| 156. C3×C5 | C2×#100 | semidirect |
| 171. C2×C5 | #823 | semidirect |
| 193. C2×C3 | #3955 | semidirect |
| 196. C5 | C2×#823 | semidirect |
| 209. C3 | C2×#3955 | semidirect |
| 213. C2 | #91107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D60 | 2 |
| C2×C3×C5×M16 | 2 |
| C2×#6710 | 2 |
| #91107 | 2 |
| C2×#3955 | 3 |
| C2×#823 | 5 |