Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
204 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 4. C3×#3996 | C2 | semidirect |
| 5. C3×#3995 | C2 | semidirect |
| 6. #65729 | C3 | direct (N × H) |
| 23. #3996 | C2×C3 | semidirect |
| 24. #3995 | C2×C3 | semidirect |
| 128. C3×C5 | #430 | semidirect |
| 157. C5 | C3×#430 | semidirect |
| 166. C3 | #65729 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5⋊M16 | 2 |
| C2×C3×#700 | 2 |
| C3×D5×M16 | 2 |
| C3×#3996 | 2 |
| C3×#3995 | 2 |
| #65729 | 3 |
| C3×#430 | 5 |