Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
244 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#6758 | C2 | semidirect |
| 3. #91232 | C2 | semidirect |
| 4. C4⋊(C3⋊#170) | C2 | semidirect |
| 5. C4×C3⋊#170 | C2 | semidirect |
| 32. C3⋊#170 | D4 | semidirect |
| 53. C3×C4×C5 | M16 | semidirect |
| 102. C4×C5 | #208 | semidirect |
| 115. C3×C5 | #436 | semidirect |
| 124. C3×C4 | #700 | semidirect |
| 144. C5 | #5012 | semidirect |
| 153. C4 | #6758 | semidirect |
| 154. C3 | #65705 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6758 | 2 |
| C3×#4039 | 2 |
| #91232 | 2 |
| C4⋊(C3⋊#170) | 2 |
| C4×C3⋊#170 | 2 |
| #65705 | 3 |
| #5012 | 5 |