Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
424 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 132 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. #91776 | C2 | semidirect |
| 3. C3×#4033 | C2 | semidirect |
| 4. C4×#1204 | C2 | semidirect |
| 5. #91389 | C2 | semidirect |
| 7. #91372 | C2 | semidirect |
| 8. #91371 | C2 | semidirect |
| 10. #91367 | C2 | semidirect |
| 11. #91352 | C2 | semidirect |
| 43. #4033 | D3 | semidirect |
| 220. C3×C5 | #556 | semidirect |
| 259. C5 | #5568 | semidirect |
| 274. C3 | #65876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #91776 | 2 |
| C5×#893 | 2 |
| C3×#4033 | 2 |
| C4×#1204 | 2 |
| #91389 | 2 |
| #91373 | 2 |
| #91372 | 2 |
| #91371 | 2 |
| #91370 | 2 |
| #91367 | 2 |
| #91352 | 2 |
| #65876 | 3 |
| #5568 | 5 |