Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
212 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×#4131 | C2 | semidirect |
| 3. C3×#4008 | C2 | semidirect |
| 4. C3×#3996 | C2 | semidirect |
| 5. C3×C8×AGL(1,𝔽5) | C2 | semidirect |
| 6. #65732 | C3 | direct (N × H) |
| 13. C3×C5×D8 | C4 | semidirect |
| 14. C3×#687 | C4 | semidirect |
| 15. C3×Dic20 | C4 | semidirect |
| 18. #4131 | C2×C3 | semidirect |
| 20. #4008 | C2×C3 | semidirect |
| 21. #3996 | C2×C3 | semidirect |
| 22. C8×AGL(1,𝔽5) | C2×C3 | semidirect |
| 45. C5×D8 | C3×C4 | semidirect |
| 46. #687 | C3×C4 | semidirect |
| 47. Dic20 | C3×C4 | semidirect |
| 59. C3×D8 | AGL(1,𝔽5) | semidirect |
| 105. D8 | C3×AGL(1,𝔽5) | semidirect |
| 112. C3×C5 | #443 | semidirect |
| 136. C5 | C3×#443 | semidirect |
| 143. C3 | #65732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4131 | 2 |
| C3×#4058 | 2 |
| C3×#4008 | 2 |
| C3×#3996 | 2 |
| C3×C8×AGL(1,𝔽5) | 2 |
| #65732 | 3 |
| C3×#443 | 5 |