Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
596 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 312 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×#704 | C2 | direct (N × H) |
| 3. C22×C3×#170 | C2 | semidirect |
| 4. C22×#704 | C3 | direct (N × H) |
| 10. C3×#704 | C22 | direct (N × H) |
| 11. C2×C3×#170 | C22 | semidirect |
| 14. C2×#704 | C2×C3 | direct (N × H) |
| 15. C22×#170 | C2×C3 | semidirect |
| 24. C3×#170 | C23 | semidirect |
| 33. #704 | C22×C3 | direct (N × H) |
| 34. C2×#170 | C22×C3 | semidirect |
| 37. C22×C3×C5 | M16 | semidirect |
| 58. #170 | C23×C3 | semidirect |
| 63. C2×C3×C5 | C2×M16 | semidirect |
| 75. C22×C5 | C3×M16 | semidirect |
| 88. C3×C5 | C22×M16 | semidirect |
| 90. C22×C3 | #704 | direct (N × H) |
| 97. C2×C5 | C2×C3×M16 | semidirect |
| 109. C2×C3 | C2×#704 | direct (N × H) |
| 111. C5 | C22×C3×M16 | semidirect |
| 113. C22 | C3×#704 | direct (N × H) |
| 119. C3 | C22×#704 | direct (N × H) |
| 121. C2 | C2×C3×#704 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Dic5 | 2 |
| C2×C3×#704 | 2 |
| C22×C3×#170 | 2 |
| C22×#704 | 3 |
| C22×C3×M16 | 5 |