Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
308 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 118 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×C5×M16 | C2 | semidirect |
| 3. C3×#4072 | C2 | semidirect |
| 4. C3×#3957 | C2 | semidirect |
| 5. #65428 | C3 | direct (N × H) |
| 10. C3×#709 | C4 | semidirect |
| 12. C2×C3×D20 | C4 | semidirect |
| 14. C2×C3×Dic10 | C4 | semidirect |
| 16. C3×C5×M16 | C22 | semidirect |
| 20. C3×C4×Dic5 | C22 | semidirect |
| 23. C2×C5×M16 | C2×C3 | semidirect |
| 24. #4072 | C2×C3 | semidirect |
| 25. #3957 | C2×C3 | semidirect |
| 46. C2×C3×M16 | D5 | semidirect |
| 53. #709 | C3×C4 | semidirect |
| 55. C2×D20 | C3×C4 | semidirect |
| 57. C2×Dic10 | C3×C4 | semidirect |
| 59. C5×M16 | C22×C3 | semidirect |
| 63. C4×Dic5 | C22×C3 | semidirect |
| 87. C3×M16 | C2×D5 | semidirect |
| 112. C2×M16 | C3×D5 | semidirect |
| 161. M16 | C2×C3×D5 | semidirect |
| 166. C3×C5 | #421 | semidirect |
| 208. C5 | C3×#421 | semidirect |
| 221. C3 | #65428 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#709 | 2 |
| C2×C3×C5×M16 | 2 |
| C3×#4072 | 2 |
| C3×#3957 | 2 |
| #65428 | 3 |
| C3×#421 | 5 |