Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
292 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 103 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. #11751002 | C2 | semidirect |
| 3. C3×C4×C5×C16 | C2 | semidirect |
| 4. #11746329 | C2 | semidirect |
| 5. #11746284 | C2 | semidirect |
| 20. C4×C5×C16 | D3 | semidirect |
| 39. C3×C4×C16 | D5 | semidirect |
| 92. C4×C16 | D15 | semidirect |
| 168. C3×C5 | #2170 | semidirect |
| 192. C5 | #69056 | semidirect |
| 199. C3 | #10599849 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751002 | 2 |
| #11750801 | 2 |
| C3×C4×C5×C16 | 2 |
| #11746329 | 2 |
| #11746284 | 2 |
| #10599849 | 3 |
| #69056 | 5 |