Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
252 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #91233 | C2 | semidirect |
| 4. C3×#4004 | C2 | semidirect |
| 5. #91177 | C2 | semidirect |
| 22. #4004 | D3 | semidirect |
| 57. Dic15 | M16 | semidirect |
| 58. C3×Dic5 | M16 | semidirect |
| 116. Dic5 | ΓL(1,𝔽25) | semidirect |
| 129. C3×C5 | #423 | semidirect |
| 162. C5 | #4837 | semidirect |
| 174. C3 | #65682 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6740 | 2 |
| C4×#1200 | 2 |
| #91233 | 2 |
| C3×#4004 | 2 |
| #91177 | 2 |
| #65682 | 3 |
| #4837 | 5 |