Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
292 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 66 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. #11751686 | C2 | semidirect |
| 3. C16×ΓL(1,𝔽16) | C2 | semidirect |
| 4. C3×#64851 | C2 | semidirect |
| 5. #11746460 | C2 | semidirect |
| 13. Dic120 | C4 | semidirect |
| 14. C5×D48 | C4 | semidirect |
| 16. #90944 | C4 | semidirect |
| 21. #64851 | D3 | semidirect |
| 72. D48 | AGL(1,𝔽5) | semidirect |
| 164. C3×C5 | #2178 | semidirect |
| 188. C5 | #69357 | semidirect |
| 195. C3 | #10604122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11751686 | 2 |
| #11746832 | 2 |
| C16×ΓL(1,𝔽16) | 2 |
| C3×#64851 | 2 |
| #11746460 | 2 |
| #10604122 | 3 |
| #69357 | 5 |