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 |
|---|---|---|
| 1. #11750781 | C2 | semidirect |
| 3. C5×#4463 | C2 | semidirect |
| 4. #11745938 | C2 | semidirect |
| 30. C3×Dic20 | Q8 | semidirect |
| 31. C3×D40 | Q8 | semidirect |
| 40. #4463 | D5 | semidirect |
| 81. Dic20 | Dic6 | semidirect |
| 82. D40 | Dic6 | semidirect |
| 172. C3×C5 | #2230 | semidirect |
| 199. C5 | #70919 | semidirect |
| 207. C3 | #10600100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750781 | 2 |
| C3×#64989 | 2 |
| C5×#4463 | 2 |
| #11745938 | 2 |
| #11745910 | 2 |
| #10600100 | 3 |
| #70919 | 5 |