Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 82 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×SD16 | C2 | semidirect |
| 2. C3×#4092 | C2 | semidirect |
| 4. C2×C3×#676 | C2 | semidirect |
| 5. C3×#3967 | C2 | semidirect |
| 6. C3×#3964 | C2 | semidirect |
| 7. C3×#3950 | C2 | semidirect |
| 8. #65463 | C3 | direct (N × H) |
| 23. C2×C5×SD16 | C2×C3 | semidirect |
| 24. #4092 | C2×C3 | semidirect |
| 26. C2×#676 | C2×C3 | semidirect |
| 27. #3967 | C2×C3 | semidirect |
| 28. #3964 | C2×C3 | semidirect |
| 29. #3950 | C2×C3 | semidirect |
| 44. C3×C5×C8 | D4 | semidirect |
| 46. C2×C3×SD16 | D5 | semidirect |
| 107. C5×C8 | C3×D4 | semidirect |
| 109. C2×SD16 | C3×D5 | semidirect |
| 136. C3×C8 | C22⋊D5 | semidirect |
| 163. C3×C5 | #468 | semidirect |
| 197. C8 | C3×C22⋊D5 | semidirect |
| 203. C5 | C3×#468 | semidirect |
| 217. C3 | #65463 | 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×SD16 | 2 |
| C3×#4092 | 2 |
| C3×#4084 | 2 |
| C2×C3×#676 | 2 |
| C3×#3967 | 2 |
| C3×#3964 | 2 |
| C3×#3950 | 2 |
| #65463 | 3 |
| C3×#468 | 5 |