Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
368 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. C3×#64991 | C2 | semidirect |
| 3. #11746922 | C2 | semidirect |
| 5. #11746286 | C2 | semidirect |
| 7. #11745849 | C2 | semidirect |
| 32. #64991 | D3 | semidirect |
| 300. C3×C5 | #1664 | semidirect |
| 340. C5 | #71394 | semidirect |
| 354. C3 | #10599152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752653 | 2 |
| C3×#64991 | 2 |
| #11746922 | 2 |
| #11746904 | 2 |
| #11746286 | 2 |
| C5×#4464 | 2 |
| #11745849 | 2 |
| #10599152 | 3 |
| #71394 | 5 |