Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
308 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 308 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×#65441 | C2 | semidirect |
| 3. #11748065 | C2 | semidirect |
| 4. C5×#4563 | C2 | semidirect |
| 5. #11745935 | C2 | semidirect |
| 6. #11745913 | C2 | semidirect |
| 7. #11745876 | C2 | semidirect |
| 13. #91111 | C4 | semidirect |
| 14. #91110 | C4 | semidirect |
| 23. #65441 | D3 | semidirect |
| 36. Dic60 | C2×C4 | semidirect |
| 37. D120 | C2×C4 | semidirect |
| 46. C3⋊#672 | C2×C4 | semidirect |
| 51. #4563 | D5 | semidirect |
| 225. C3×C5 | AGL(1,ℤ/16) | semidirect |
| 259. C5 | #70918 | semidirect |
| 270. C3 | #10600047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751248 | 2 |
| C3×#65441 | 2 |
| #11748065 | 2 |
| C5×#4563 | 2 |
| #11745935 | 2 |
| #11745913 | 2 |
| #11745876 | 2 |
| #10600047 | 3 |
| #70918 | 5 |