Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
424 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 246 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 |
|---|---|---|
| 6. Q8×Dic10 | C3 | direct (N × H) |
| 22. C3×C5×Q8 | Q8 | semidirect |
| 29. C3×Dic10 | Q8 | direct (N × H) |
| 60. C5×Q8 | C3×Q8 | semidirect |
| 67. Dic10 | C3×Q8 | direct (N × H) |
| 78. C3×Q8 | Dic10 | direct (N × H) |
| 99. C3×C5 | Q82 | semidirect |
| 111. Q8 | C3×Dic10 | direct (N × H) |
| 120. C5 | C3×Q82 | semidirect |
| 127. C3 | Q8×Dic10 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C5×Q8 | 2 |
| C3×Q8×Dic5 | 2 |
| C3×#4034 | 2 |
| C3×#4015 | 2 |
| C3×C4×Dic10 | 2 |
| Q8×Dic10 | 3 |
| C3×Q82 | 5 |