Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
296 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 296 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 |
|---|---|---|
| 2. C2×C3×C5×Q16 | C2 | semidirect |
| 4. C2×C3×#689 | C2 | semidirect |
| 5. C3×#3967 | C2 | semidirect |
| 7. C3×#3948 | C2 | semidirect |
| 8. #65475 | C3 | direct (N × H) |
| 26. C2×C5×Q16 | C2×C3 | semidirect |
| 28. C2×#689 | C2×C3 | semidirect |
| 29. #3967 | C2×C3 | semidirect |
| 31. #3948 | C2×C3 | semidirect |
| 53. C2×C3×Q16 | D5 | semidirect |
| 77. C2×C3×D5 | Q16 | semidirect |
| 121. C2×Q16 | C3×D5 | semidirect |
| 152. C2×D5 | C3×Q16 | semidirect |
| 175. C3×C5 | #451 | semidirect |
| 214. C5 | C3×#451 | semidirect |
| 226. C3 | #65475 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×D5 | 2 |
| C2×C3×C5×Q16 | 2 |
| C3×#4092 | 2 |
| C2×C3×#689 | 2 |
| C3×#3967 | 2 |
| C3×#3952 | 2 |
| C3×#3948 | 2 |
| #65475 | 3 |
| C3×#451 | 5 |