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. C3×#4090 | C2 | semidirect |
| 5. C3×C5×#103 | C2 | semidirect |
| 6. C3×#3946 | C2 | semidirect |
| 7. C3×#3942 | C2 | semidirect |
| 8. #65107 | C3 | direct (N × H) |
| 23. #4090 | C2×C3 | semidirect |
| 27. C5×#103 | C2×C3 | semidirect |
| 28. #3946 | C2×C3 | semidirect |
| 29. #3942 | C2×C3 | semidirect |
| 52. C3×#103 | D5 | semidirect |
| 77. C3×Dic5 | SD16 | semidirect |
| 113. #103 | C3×D5 | semidirect |
| 144. Dic5 | C3×SD16 | semidirect |
| 158. C3×C5 | #461 | semidirect |
| 194. C5 | C3×#461 | semidirect |
| 206. C3 | #65107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4090 | 2 |
| C2×C3×#688 | 2 |
| C2×C3×#677 | 2 |
| C3×#4039 | 2 |
| C3×C5×#103 | 2 |
| C3×#3946 | 2 |
| C3×#3942 | 2 |
| #65107 | 3 |
| C3×#461 | 5 |