Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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. #11751013 | C2 | semidirect |
| 2. C3×C5×D32 | C2 | semidirect |
| 3. #11746341 | C2 | semidirect |
| 4. Dic240 | C2 | semidirect |
| 5. D15×C32 | C2 | semidirect |
| 16. C5×D32 | D3 | semidirect |
| 28. C3×D32 | D5 | semidirect |
| 64. D32 | D15 | semidirect |
| 114. C3×C5 | #2262 | semidirect |
| 133. C5 | #69376 | semidirect |
| 139. C3 | #10600169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751013 | 2 |
| C3×C5×D32 | 2 |
| #11746341 | 2 |
| Dic240 | 2 |
| D15×C32 | 2 |
| #10600169 | 3 |
| #69376 | 5 |