Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
516 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 136 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×D15⋊Q8 | C2 | semidirect |
| 3. C2×#6705 | C2 | semidirect |
| 4. C2×C5×#204 | C2 | semidirect |
| 5. C2×C3×Dic20 | C2 | semidirect |
| 6. C2×#6661 | C2 | semidirect |
| 7. C2×#6656 | C2 | semidirect |
| 8. #91280 | C2 | direct (N × H) |
| 20. D15⋊Q8 | C22 | semidirect |
| 25. #6705 | C22 | semidirect |
| 26. C5×#204 | C22 | semidirect |
| 27. C3×Dic20 | C22 | semidirect |
| 28. #6661 | C22 | semidirect |
| 29. #6656 | C22 | semidirect |
| 37. C2×Dic20 | D3 | semidirect |
| 68. C2×#204 | D5 | semidirect |
| 88. Dic20 | C2×D3 | semidirect |
| 120. #204 | C2×D5 | semidirect |
| 153. C2×C3×C5 | #137 | semidirect |
| 211. C3×C5 | C2×#137 | semidirect |
| 224. C2×C5 | #918 | semidirect |
| 250. C2×C3 | #4061 | semidirect |
| 254. C5 | C2×#918 | semidirect |
| 266. C3 | C2×#4061 | semidirect |
| 269. C2 | #91280 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D15⋊Q8 | 2 |
| C2×#6768 | 2 |
| C2×#6705 | 2 |
| C2×C5×#204 | 2 |
| C2×C3×Dic20 | 2 |
| C2×#6661 | 2 |
| C2×#6656 | 2 |
| #91280 | 2 |
| C2×#4061 | 3 |
| C2×#918 | 5 |