Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
240 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 86 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×M16 | C2 | semidirect |
| 3. C3×#4070 | C2 | semidirect |
| 4. C2×C3×#677 | C2 | semidirect |
| 5. C3×#3953 | C2 | semidirect |
| 6. C3×#3950 | C2 | semidirect |
| 7. C3×#3948 | C2 | semidirect |
| 8. #65423 | C3 | direct (N × H) |
| 23. C2×C5×M16 | C2×C3 | semidirect |
| 25. #4070 | C2×C3 | semidirect |
| 26. C2×#677 | C2×C3 | semidirect |
| 27. #3953 | C2×C3 | semidirect |
| 28. #3950 | C2×C3 | semidirect |
| 29. #3948 | C2×C3 | semidirect |
| 45. C3×C5×C8 | D4 | semidirect |
| 47. C2×C3×M16 | D5 | semidirect |
| 108. C5×C8 | C3×D4 | semidirect |
| 110. C2×M16 | 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 | #65423 | 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×M16 | 2 |
| C3×#4076 | 2 |
| C3×#4070 | 2 |
| C2×C3×#677 | 2 |
| C3×#3953 | 2 |
| C3×#3950 | 2 |
| C3×#3948 | 2 |
| #65423 | 3 |
| C3×#468 | 5 |