Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
288 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 84 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. #11748064 | C2 | semidirect |
| 3. C5×#4506 | C2 | semidirect |
| 4. C3×#64722 | C2 | semidirect |
| 5. #11745908 | C2 | semidirect |
| 10. Dic120 | C4 | semidirect |
| 11. #91084 | C4 | semidirect |
| 12. D240 | C4 | semidirect |
| 21. #64722 | D3 | semidirect |
| 40. #4506 | D5 | semidirect |
| 161. C3×C5 | #2179 | semidirect |
| 184. C5 | #69085 | semidirect |
| 191. C3 | #10600151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751005 | 2 |
| #11748064 | 2 |
| C5×#4506 | 2 |
| C3×#64722 | 2 |
| #11745908 | 2 |
| #10600151 | 3 |
| #69085 | 5 |