Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
224 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 2. C2×C3×#689 | C2 | semidirect |
| 4. C3×#4033 | C2 | semidirect |
| 5. C3×C5×#103 | C2 | semidirect |
| 6. C3×#3946 | C2 | semidirect |
| 8. #65087 | C3 | direct (N × H) |
| 24. C2×#689 | C2×C3 | semidirect |
| 26. #4033 | C2×C3 | semidirect |
| 27. C5×#103 | C2×C3 | semidirect |
| 28. #3946 | C2×C3 | semidirect |
| 50. C3×#103 | D5 | semidirect |
| 110. #103 | C3×D5 | semidirect |
| 155. C3×C5 | #464 | semidirect |
| 190. C5 | C3×#464 | semidirect |
| 202. C3 | #65087 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4093 | 2 |
| C2×C3×#689 | 2 |
| C2×C3×#677 | 2 |
| C3×#4033 | 2 |
| C3×C5×#103 | 2 |
| C3×#3946 | 2 |
| C3×#3941 | 2 |
| #65087 | 3 |
| C3×#464 | 5 |