Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
308 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 74 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. #91989 | C2 | semidirect |
| 3. C3×D5⋊M16 | C2 | semidirect |
| 4. #91155 | C2 | semidirect |
| 6. C2×Dic30 | C4 | semidirect |
| 7. C2×C5×D12 | C4 | semidirect |
| 13. #6772 | C4 | semidirect |
| 17. C4×ΓL(1,𝔽16) | C22 | semidirect |
| 19. C3×#700 | C22 | semidirect |
| 24. D5⋊M16 | D3 | semidirect |
| 62. #700 | C2×D3 | semidirect |
| 83. C2×D12 | AGL(1,𝔽5) | semidirect |
| 166. C3×C5 | #421 | semidirect |
| 208. C5 | #5139 | semidirect |
| 221. C3 | #65769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6772 | 2 |
| #91989 | 2 |
| C3×D5⋊M16 | 2 |
| #91155 | 2 |
| #65769 | 3 |
| #5139 | 5 |