Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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×#6706 | C2 | semidirect |
| 2. C2×C3×#677 | C2 | semidirect |
| 3. #91374 | C2 | semidirect |
| 4. #91364 | C2 | semidirect |
| 5. C2×#6662 | C2 | semidirect |
| 7. C5×C8×Dic3 | C2 | semidirect |
| 26. C2×#677 | D3 | semidirect |
| 52. C8×Dic3 | D5 | semidirect |
| 156. C3×C5 | #495 | semidirect |
| 191. C5 | #5168 | semidirect |
| 202. C3 | #64985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6706 | 2 |
| C2×C3×#677 | 2 |
| #91374 | 2 |
| #91364 | 2 |
| C2×#6662 | 2 |
| C2×#6653 | 2 |
| C5×C8×Dic3 | 2 |
| #64985 | 3 |
| #5168 | 5 |