Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
456 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 140 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. C5×#888 | C2 | semidirect |
| 3. C3×#4036 | C2 | semidirect |
| 4. C4×#1204 | C2 | semidirect |
| 5. #91429 | C2 | semidirect |
| 7. #91424 | C2 | semidirect |
| 9. #91404 | C2 | semidirect |
| 10. #91384 | C2 | semidirect |
| 11. #91383 | C2 | semidirect |
| 45. #4036 | D3 | semidirect |
| 53. D60 | Q8 | semidirect |
| 73. #888 | D5 | semidirect |
| 223. C3×C5 | #554 | semidirect |
| 263. C5 | #5690 | semidirect |
| 278. C3 | #66064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91782 | 2 |
| C5×#888 | 2 |
| C3×#4036 | 2 |
| C4×#1204 | 2 |
| #91429 | 2 |
| #91428 | 2 |
| #91424 | 2 |
| #91418 | 2 |
| #91404 | 2 |
| #91384 | 2 |
| #91383 | 2 |
| #66064 | 3 |
| #5690 | 5 |