Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
596 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 280 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. #91344 | C2 | direct (N × H) |
| 12. C2×C5×Dic6 | C4 | semidirect |
| 30. C2×Dic15 | Q8 | semidirect |
| 35. C5×Dic6 | C2×C4 | semidirect |
| 62. Dic15 | C2×Q8 | semidirect |
| 70. C2×Dic6 | Dic5 | semidirect |
| 94. C2×C3×C5 | C4×Q8 | semidirect |
| 109. Dic6 | C2×Dic5 | semidirect |
| 130. C3×C5 | C2×C4×Q8 | semidirect |
| 140. C2×C5 | #887 | semidirect |
| 156. C2×C3 | Q8×Dic5 | semidirect |
| 160. C5 | C2×#887 | semidirect |
| 170. C3 | C2×Q8×Dic5 | semidirect |
| 171. C2 | #91344 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic6 | 2 |
| C2×C4×Dic15 | 2 |
| C2×C3×C4⋊Dic5 | 2 |
| C2×Dic3⋊Dic5 | 2 |
| C2×Dic3×Dic5 | 2 |
| #91344 | 2 |
| C2×Q8×Dic5 | 3 |
| C2×#887 | 5 |