Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
540 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 171 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 | semidirect |
| 4. #91835 | C2 | semidirect |
| 5. #91833 | C2 | semidirect |
| 6. #91818 | C2 | semidirect |
| 7. #91815 | C2 | semidirect |
| 25. C22×C5×Q8 | D3 | semidirect |
| 47. C22×C3×Q8 | D5 | semidirect |
| 111. C22×Q8 | D15 | semidirect |
| 161. C3×C5 | #536 | semidirect |
| 195. C5 | #5816 | semidirect |
| 206. C3 | #66150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q8 | 2 |
| C2×#6817 | 2 |
| #91836 | 2 |
| #91835 | 2 |
| #91833 | 2 |
| #91818 | 2 |
| #91815 | 2 |
| #66150 | 3 |
| #5816 | 5 |