Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 240 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. #11750784 | C2 | semidirect |
| 3. C3×#64683 | C2 | semidirect |
| 4. #11745934 | C2 | semidirect |
| 21. #64683 | D3 | semidirect |
| 165. C3×C5 | #2231 | semidirect |
| 191. C5 | #69308 | semidirect |
| 199. C3 | #10601713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11750784 | 2 |
| C5×#4700 | 2 |
| C3×#64683 | 2 |
| #11745934 | 2 |
| #11745912 | 2 |
| #10601713 | 3 |
| #69308 | 5 |