Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 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. C3×#3963 | C2 | semidirect |
| 4. #65520 | C3 | direct (N × H) |
| 11. C22×C5×Q8 | C2×C3 | semidirect |
| 13. #3963 | C2×C3 | semidirect |
| 17. C22×C3×D5 | Q8 | semidirect |
| 23. C22×C3×Q8 | D5 | semidirect |
| 48. C22×D5 | C3×Q8 | semidirect |
| 54. C22×Q8 | C3×D5 | semidirect |
| 83. C3×C5 | #393 | semidirect |
| 109. C5 | C3×#393 | semidirect |
| 118. C3 | #65520 | 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 |
| C2×C3×#685 | 2 |
| C3×#3963 | 2 |
| #65520 | 3 |
| C3×#393 | 5 |