Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
660 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 203 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. C22×C3×C5×Q8 | C2 | semidirect |
| 3. #91836 | C2 | direct (N × H) |
| 4. C2×#6714 | C2 | semidirect |
| 5. C2×C4×Dic15 | C2 | semidirect |
| 9. C2×C3×C5×Q8 | C22 | semidirect |
| 15. #6714 | C22 | semidirect |
| 16. C4×Dic15 | C22 | semidirect |
| 18. C22×C5×Q8 | D3 | semidirect |
| 35. C22×C3×Q8 | D5 | semidirect |
| 42. C2×C5×Q8 | C2×D3 | semidirect |
| 62. C2×C3×Q8 | C2×D5 | semidirect |
| 82. C22×Q8 | D15 | semidirect |
| 87. C2×C3×C5 | #124 | semidirect |
| 114. C2×Q8 | C2×D15 | semidirect |
| 122. C3×C5 | C2×#124 | semidirect |
| 132. C2×C5 | #947 | semidirect |
| 148. C2×C3 | #4093 | semidirect |
| 152. C5 | C2×#947 | semidirect |
| 162. C3 | C2×#4093 | semidirect |
| 164. C2 | #91836 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q8 | 2 |
| C22×D60 | 2 |
| #91836 | 2 |
| C2×#6714 | 2 |
| C2×C4×Dic15 | 2 |
| C2×#4093 | 3 |
| C2×#947 | 5 |