Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
316 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 126 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. C22×C3×C5×C8 | C2 | semidirect |
| 3. C3×#4072 | C2 | semidirect |
| 4. C3×#3953 | C2 | semidirect |
| 5. C3×#3948 | C2 | semidirect |
| 6. #65402 | C3 | direct (N × H) |
| 10. C3×#709 | C4 | semidirect |
| 21. C22×C5×C8 | C2×C3 | semidirect |
| 22. #4072 | C2×C3 | semidirect |
| 23. #3953 | C2×C3 | semidirect |
| 24. #3948 | C2×C3 | semidirect |
| 41. C22×C3×C8 | D5 | semidirect |
| 48. #709 | C3×C4 | semidirect |
| 96. C22×C8 | C3×D5 | semidirect |
| 141. C3×C5 | #416 | semidirect |
| 175. C5 | C3×#416 | semidirect |
| 186. C3 | #65402 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#709 | 2 |
| C22×C3×C5×C8 | 2 |
| C3×#4072 | 2 |
| C3×#3953 | 2 |
| C3×#3948 | 2 |
| #65402 | 3 |
| C3×#416 | 5 |