Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
268 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 90 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×C5×#121 | C2 | semidirect |
| 2. C2×C3×#686 | C2 | semidirect |
| 3. C3×#4076 | C2 | semidirect |
| 4. C22×C3×#168 | C2 | semidirect |
| 5. C3×#3964 | C2 | semidirect |
| 6. C3×#3941 | C2 | semidirect |
| 7. C3×#3939 | C2 | semidirect |
| 8. #65327 | C3 | direct (N × H) |
| 23. C5×#121 | C2×C3 | semidirect |
| 24. C2×#686 | C2×C3 | semidirect |
| 25. #4076 | C2×C3 | semidirect |
| 26. C22×#168 | C2×C3 | semidirect |
| 27. #3964 | C2×C3 | semidirect |
| 28. #3941 | C2×C3 | semidirect |
| 29. #3939 | C2×C3 | semidirect |
| 46. C3×#168 | D4 | semidirect |
| 50. C3×#121 | D5 | semidirect |
| 73. C22×C3×C5 | D8 | semidirect |
| 112. #168 | C3×D4 | semidirect |
| 116. #121 | C3×D5 | semidirect |
| 148. C22×C5 | C3×D8 | semidirect |
| 171. C3×C5 | #466 | semidirect |
| 180. C22×C3 | #686 | semidirect |
| 216. C5 | C3×#466 | semidirect |
| 225. C22 | C3×#686 | semidirect |
| 232. C3 | #65327 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#121 | 2 |
| C2×C3×#686 | 2 |
| C3×#4076 | 2 |
| C22×C3×#168 | 2 |
| C3×#3964 | 2 |
| C3×#3941 | 2 |
| C3×#3939 | 2 |
| #65327 | 3 |
| C3×#466 | 5 |