Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
252 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 78 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. C5×#4463 | C2 | semidirect |
| 4. #11745937 | C2 | semidirect |
| 18. #64969 | D3 | semidirect |
| 28. Dic60 | Q8 | semidirect |
| 29. D120 | Q8 | semidirect |
| 40. #4463 | D5 | semidirect |
| 172. C3×C5 | #2230 | semidirect |
| 199. C5 | #71350 | semidirect |
| 207. C3 | #10600100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750801 | 2 |
| C3×#64969 | 2 |
| C5×#4463 | 2 |
| #11745937 | 2 |
| #11745913 | 2 |
| #10600100 | 3 |
| #71350 | 5 |