Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
164 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 62 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. C3×D5×Q16 | C2 | semidirect |
| 3. C3×C5×Q32 | C2 | semidirect |
| 4. C3×#3961 | C2 | semidirect |
| 5. C3×#3960 | C2 | semidirect |
| 6. C3×#3932 | C2 | semidirect |
| 7. C3×#3930 | C2 | semidirect |
| 8. #65207 | C3 | direct (N × H) |
| 22. D5×Q16 | C2×C3 | semidirect |
| 23. C5×Q32 | C2×C3 | semidirect |
| 24. #3961 | C2×C3 | semidirect |
| 25. #3960 | C2×C3 | semidirect |
| 26. #3932 | C2×C3 | semidirect |
| 27. #3930 | C2×C3 | semidirect |
| 42. C3×Q32 | D5 | semidirect |
| 90. Q32 | C3×D5 | semidirect |
| 126. C3×C5 | #510 | semidirect |
| 151. C5 | C3×#510 | semidirect |
| 159. C3 | #65207 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4065 | 2 |
| C3×D5×Q16 | 2 |
| C3×C5×Q32 | 2 |
| C3×#3961 | 2 |
| C3×#3960 | 2 |
| C3×#3932 | 2 |
| C3×#3930 | 2 |
| #65207 | 3 |
| C3×#510 | 5 |