Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 336 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. C3×#64968 | C2 | semidirect |
| 4. C5×#4454 | C2 | semidirect |
| 5. #11745869 | C2 | semidirect |
| 6. #11745841 | C2 | semidirect |
| 27. #64968 | D3 | semidirect |
| 56. #4454 | D5 | semidirect |
| 252. C3×C5 | #1585 | semidirect |
| 293. C5 | #70954 | semidirect |
| 306. C3 | #10598873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D60 | 2 |
| C3×#64968 | 2 |
| C4×#6658 | 2 |
| C5×#4454 | 2 |
| #11745869 | 2 |
| #11745841 | 2 |
| #11745838 | 2 |
| #10598873 | 3 |
| #70954 | 5 |