Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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. #91990 | C2 | semidirect |
| 3. #91237 | C2 | semidirect |
| 4. #91225 | C2 | semidirect |
| 5. C8×ΓL(1,𝔽16) | C2 | semidirect |
| 13. C3×C5×D8 | C4 | semidirect |
| 14. C3×#687 | C4 | semidirect |
| 15. C3×Dic20 | C4 | semidirect |
| 45. C5×D8 | Dic3 | semidirect |
| 46. #687 | Dic3 | semidirect |
| 47. Dic20 | Dic3 | semidirect |
| 59. C3×D8 | AGL(1,𝔽5) | semidirect |
| 105. D8 | ΓL(1,𝔽16) | semidirect |
| 112. C3×C5 | #443 | semidirect |
| 136. C5 | #5196 | semidirect |
| 143. C3 | #65732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91990 | 2 |
| C3×#4058 | 2 |
| #91237 | 2 |
| #91225 | 2 |
| C8×ΓL(1,𝔽16) | 2 |
| #65732 | 3 |
| #5196 | 5 |