Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
180 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 70 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×D8 | C2 | semidirect |
| 2. C3×#4050 | C2 | semidirect |
| 3. C3×#3959 | C2 | semidirect |
| 4. C3×#3958 | C2 | semidirect |
| 5. C3×#3944 | C2 | semidirect |
| 6. #65436 | C3 | direct (N × H) |
| 12. C3×Dic20 | C22 | semidirect |
| 13. C3×D40 | C22 | semidirect |
| 15. C3×#672 | C22 | semidirect |
| 17. C2×C5×D8 | C2×C3 | semidirect |
| 18. #4050 | C2×C3 | semidirect |
| 19. #3959 | C2×C3 | semidirect |
| 20. #3958 | C2×C3 | semidirect |
| 21. #3944 | C2×C3 | semidirect |
| 33. C2×C3×D8 | D5 | semidirect |
| 42. Dic20 | C22×C3 | semidirect |
| 43. D40 | C22×C3 | semidirect |
| 45. #672 | C22×C3 | semidirect |
| 74. C2×D8 | C3×D5 | semidirect |
| 108. C3×C5 | #509 | semidirect |
| 134. C5 | C3×#509 | semidirect |
| 142. C3 | #65436 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×D8 | 2 |
| C3×#4050 | 2 |
| C3×#3959 | 2 |
| C3×#3958 | 2 |
| C3×#3944 | 2 |
| #65436 | 3 |
| C3×#509 | 5 |