Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 92 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×#704 | C2 | semidirect |
| 2. C2×C3×#700 | C2 | semidirect |
| 4. C3×C22⋊#170 | C2 | semidirect |
| 5. C3×#4004 | C2 | semidirect |
| 6. C3×#4003 | C2 | semidirect |
| 7. C3×C4×#170 | C2 | semidirect |
| 8. #65695 | C3 | direct (N × H) |
| 23. C2×#704 | C2×C3 | semidirect |
| 24. C2×#700 | C2×C3 | semidirect |
| 26. C22⋊#170 | C2×C3 | semidirect |
| 27. #4004 | C2×C3 | semidirect |
| 28. #4003 | C2×C3 | semidirect |
| 29. C4×#170 | C2×C3 | semidirect |
| 45. C3×#170 | D4 | semidirect |
| 77. C3×Dic5 | M16 | semidirect |
| 108. #170 | C3×D4 | semidirect |
| 147. Dic5 | C3×M16 | semidirect |
| 163. C3×C5 | #436 | semidirect |
| 203. C5 | C3×#436 | semidirect |
| 217. C3 | #65695 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#704 | 2 |
| C2×C3×#700 | 2 |
| C3×#4027 | 2 |
| C3×C22⋊#170 | 2 |
| C3×#4004 | 2 |
| C3×#4003 | 2 |
| C3×C4×#170 | 2 |
| #65695 | 3 |
| C3×#436 | 5 |