Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
164 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 49 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. C3×C5×Q32 | C2 | semidirect |
| 3. #91113 | C2 | semidirect |
| 4. Dic120 | C2 | semidirect |
| 16. C5×Q32 | D3 | semidirect |
| 28. C3×Q32 | D5 | semidirect |
| 62. Q32 | D15 | direct (N × H) |
| 65. D15 | Q32 | direct (N × H) |
| 85. C3×C5 | C2×Q32 | semidirect |
| 102. C5 | D3×Q32 | semidirect |
| 108. C3 | D5×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D15 | 2 |
| C3×C5×Q32 | 2 |
| #91113 | 2 |
| Dic120 | 2 |
| C16×D15 | 2 |
| D5×Q32 | 3 |
| D3×Q32 | 5 |