Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
324 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×C3×C4⋊Dic5 | C2 | semidirect |
| 4. C3×#3953 | C2 | semidirect |
| 5. C3×#3948 | C2 | semidirect |
| 6. #65422 | C3 | direct (N × H) |
| 11. C3×#709 | C4 | semidirect |
| 21. C2×C5×M16 | C2×C3 | semidirect |
| 22. C2×C4⋊Dic5 | C2×C3 | semidirect |
| 23. #3953 | C2×C3 | semidirect |
| 24. #3948 | C2×C3 | semidirect |
| 36. C3×D20 | C2×C4 | semidirect |
| 39. C3×Dic10 | C2×C4 | semidirect |
| 42. C2×C3×M16 | D5 | semidirect |
| 50. #709 | C3×C4 | semidirect |
| 94. D20 | C2×C3×C4 | semidirect |
| 97. Dic10 | C2×C3×C4 | semidirect |
| 100. C2×M16 | C3×D5 | semidirect |
| 149. C3×C5 | #417 | semidirect |
| 188. C5 | C3×#417 | semidirect |
| 201. C3 | #65422 | 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 |
| C2×C3×C4⋊Dic5 | 2 |
| C3×#3953 | 2 |
| C3×#3948 | 2 |
| #65422 | 3 |
| C3×#417 | 5 |