Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
292 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 78 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. C3×#4147 | C2 | semidirect |
| 2. C3×C5×#124 | C2 | semidirect |
| 3. C3×#4078 | C2 | semidirect |
| 4. C3×#3968 | C2 | semidirect |
| 5. C3×#3937 | C2 | semidirect |
| 6. #65351 | C3 | direct (N × H) |
| 19. #4147 | C2×C3 | semidirect |
| 20. C5×#124 | C2×C3 | semidirect |
| 21. #4078 | C2×C3 | semidirect |
| 22. #3968 | C2×C3 | semidirect |
| 23. #3937 | C2×C3 | semidirect |
| 40. C3×#124 | D5 | semidirect |
| 90. #124 | C3×D5 | semidirect |
| 130. C3×C5 | #454 | semidirect |
| 161. C5 | C3×#454 | semidirect |
| 170. C3 | #65351 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4147 | 2 |
| C3×C5×#124 | 2 |
| C3×#4078 | 2 |
| C3×#3968 | 2 |
| C3×#3937 | 2 |
| #65351 | 3 |
| C3×#454 | 5 |