Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
412 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 70 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. #11752653 | C2 | semidirect |
| 2. #11751172 | C2 | semidirect |
| 4. C3×#65360 | C2 | semidirect |
| 5. #11745851 | C2 | semidirect |
| 6. #11745849 | C2 | semidirect |
| 7. #11745847 | C2 | semidirect |
| 32. #65360 | D3 | semidirect |
| 322. C3×C5 | #1657 | semidirect |
| 369. C5 | #71249 | semidirect |
| 385. C3 | #10602121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752653 | 2 |
| #11751172 | 2 |
| C5×#5074 | 2 |
| C3×#65360 | 2 |
| #11745851 | 2 |
| #11745849 | 2 |
| #11745847 | 2 |
| #10602121 | 3 |
| #71249 | 5 |