Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 122 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×#65682 | C2 | semidirect |
| 4. C2×#91157 | C2 | semidirect |
| 5. C2×#91155 | C2 | semidirect |
| 12. #91764 | C4 | semidirect |
| 13. C5×#875 | C4 | semidirect |
| 15. #91451 | C4 | semidirect |
| 18. #91376 | C4 | semidirect |
| 27. #65682 | D3 | semidirect |
| 46. C4×ΓL(1,𝔽16) | D4 | semidirect |
| 111. #875 | AGL(1,𝔽5) | semidirect |
| 162. C3×Dic5 | #104 | semidirect |
| 278. Dic5 | #825 | semidirect |
| 309. C3×C5 | #1962 | semidirect |
| 361. C5 | #70512 | semidirect |
| 377. C3 | #10604559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752673 | 2 |
| C42×ΓL(1,𝔽16) | 2 |
| C3×#65682 | 2 |
| C2×#91157 | 2 |
| C2×#91155 | 2 |
| #10604559 | 3 |
| #70512 | 5 |