Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
228 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #91098 | C2 | semidirect |
| 93. C3×C5 | #424 | semidirect |
| 115. C5 | #5119 | semidirect |
| 123. C3 | #65408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×M16 | 2 |
| #91815 | 2 |
| C22×C3⋊#168 | 2 |
| #91098 | 2 |
| #65408 | 3 |
| #5119 | 5 |