Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
568 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 114 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. C4×C4⋊ΓL(1,𝔽16) | C2 | semidirect |
| 3. C3×#65678 | C2 | semidirect |
| 4. #11746499 | C2 | semidirect |
| 5. #11746498 | C2 | semidirect |
| 10. C4×D60 | C4 | semidirect |
| 11. C4×C5×D12 | C4 | semidirect |
| 13. #91468 | C4 | semidirect |
| 14. #91451 | C4 | semidirect |
| 27. #65678 | D3 | semidirect |
| 123. C4×D12 | AGL(1,𝔽5) | semidirect |
| 345. C3×C5 | #1502 | semidirect |
| 410. C5 | #70789 | semidirect |
| 431. C3 | #10604389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752671 | 2 |
| C4×C4⋊ΓL(1,𝔽16) | 2 |
| C3×#65678 | 2 |
| #11746499 | 2 |
| #11746498 | 2 |
| #10604389 | 3 |
| #70789 | 5 |