Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
628 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 100 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. #11751177 | C2 | semidirect |
| 3. #11746883 | C2 | semidirect |
| 4. C3×#64764 | C2 | semidirect |
| 5. #11745836 | C2 | semidirect |
| 10. #91758 | C22 | semidirect |
| 14. C4×C3⋊#168 | C22 | semidirect |
| 15. C3×C4⋊#168 | C22 | semidirect |
| 22. #64764 | D3 | semidirect |
| 55. C4⋊#168 | C2×D3 | semidirect |
| 72. C5×D12 | SD16 | semidirect |
| 186. D12 | #687 | semidirect |
| 221. C3×C5 | #1629 | semidirect |
| 261. C5 | #68391 | semidirect |
| 274. C3 | #10602700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5717 | 2 |
| #11751177 | 2 |
| #11746883 | 2 |
| C3×#64764 | 2 |
| #11745836 | 2 |
| #10602700 | 3 |
| #68391 | 5 |