Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
252 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 2. C3×#64969 | C2 | semidirect |
| 3. #11746284 | C2 | semidirect |
| 4. #11745935 | C2 | semidirect |
| 18. #64969 | D3 | semidirect |
| 28. C5×Dic12 | Q8 | semidirect |
| 29. C5×D24 | Q8 | semidirect |
| 107. Dic12 | Dic10 | semidirect |
| 108. D24 | Dic10 | semidirect |
| 172. C3×C5 | #2230 | semidirect |
| 199. C5 | #71350 | semidirect |
| 207. C3 | #10601712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4700 | 2 |
| C3×#64969 | 2 |
| #11746284 | 2 |
| #11745935 | 2 |
| #11745911 | 2 |
| #10601712 | 3 |
| #71350 | 5 |