Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
300 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×#6762 | C2 | semidirect |
| 3. C2×C3×#704 | C2 | semidirect |
| 4. #91175 | C2 | semidirect |
| 5. #91174 | C2 | semidirect |
| 27. C2×#704 | D3 | semidirect |
| 201. C3×C5 | #413 | semidirect |
| 253. C5 | #5132 | semidirect |
| 268. C3 | #65777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6782 | 2 |
| C2×#6762 | 2 |
| C2×C3×#704 | 2 |
| #91175 | 2 |
| #91174 | 2 |
| #65777 | 3 |
| #5132 | 5 |