Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 130 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. C42×ΓL(1,𝔽16) | C2 | semidirect |
| 3. C3×#65681 | C2 | semidirect |
| 4. C2×#91155 | C2 | semidirect |
| 10. #91758 | C4 | semidirect |
| 11. C5×#874 | C4 | semidirect |
| 15. #91373 | C4 | semidirect |
| 22. #65681 | D3 | semidirect |
| 35. C4×ΓL(1,𝔽16) | D4 | semidirect |
| 86. #874 | AGL(1,𝔽5) | semidirect |
| 121. C3×C4×C5 | #104 | semidirect |
| 207. C4×C5 | #825 | semidirect |
| 233. C3×C5 | #1962 | semidirect |
| 242. C3×C4 | #4008 | semidirect |
| 273. C5 | #70512 | semidirect |
| 284. C4 | #91155 | semidirect |
| 286. C3 | #10604611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752672 | 2 |
| C42×ΓL(1,𝔽16) | 2 |
| C3×#65681 | 2 |
| C2×#91155 | 2 |
| #10604611 | 3 |
| #70512 | 5 |