Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 168 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 |
|---|---|---|
| 1. C3×#4065 | C2 | semidirect |
| 2. C3×#4058 | C2 | semidirect |
| 3. C3×C5×SD32 | C2 | semidirect |
| 4. C3×#3961 | C2 | semidirect |
| 5. C3×#3958 | C2 | semidirect |
| 6. C3×#3932 | C2 | semidirect |
| 7. C3×D5×C16 | C2 | semidirect |
| 8. #65205 | C3 | direct (N × H) |
| 21. #4065 | C2×C3 | semidirect |
| 22. #4058 | C2×C3 | semidirect |
| 23. C5×SD32 | C2×C3 | semidirect |
| 24. #3961 | C2×C3 | semidirect |
| 25. #3958 | C2×C3 | semidirect |
| 26. #3932 | C2×C3 | semidirect |
| 27. D5×C16 | C2×C3 | semidirect |
| 43. C3×SD32 | D5 | semidirect |
| 91. SD32 | C3×D5 | semidirect |
| 127. C3×C5 | #508 | semidirect |
| 154. C5 | C3×#508 | semidirect |
| 162. C3 | #65205 | 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×#4058 | 2 |
| C3×C5×SD32 | 2 |
| C3×#3961 | 2 |
| C3×#3958 | 2 |
| C3×#3932 | 2 |
| C3×D5×C16 | 2 |
| #65205 | 3 |
| C3×#508 | 5 |