Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
164 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 70 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×C5×Q16 | C2 | semidirect |
| 3. C3×#3961 | C2 | semidirect |
| 4. C3×#3960 | C2 | semidirect |
| 5. C3×#3944 | C2 | semidirect |
| 6. #65468 | C3 | direct (N × H) |
| 17. C2×C5×Q16 | C2×C3 | semidirect |
| 19. #3961 | C2×C3 | semidirect |
| 20. #3960 | C2×C3 | semidirect |
| 21. #3944 | C2×C3 | semidirect |
| 33. C2×C3×Q16 | D5 | semidirect |
| 73. C2×Q16 | C3×D5 | semidirect |
| 105. C3×C5 | #510 | semidirect |
| 128. C5 | C3×#510 | semidirect |
| 135. C3 | #65468 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Q16 | 2 |
| C3×#4050 | 2 |
| C3×#3961 | 2 |
| C3×#3960 | 2 |
| C3×#3944 | 2 |
| #65468 | 3 |
| C3×#510 | 5 |