Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 364 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. #11752488 | C2 | semidirect |
| 5. #11746286 | C2 | semidirect |
| 6. C3×#64685 | C2 | semidirect |
| 7. #11745850 | C2 | semidirect |
| 35. #64685 | D3 | semidirect |
| 294. C3×C5 | #1658 | semidirect |
| 332. C5 | #68375 | semidirect |
| 346. C3 | #10602043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752488 | 2 |
| C5×#4713 | 2 |
| #11746908 | 2 |
| #11746905 | 2 |
| #11746286 | 2 |
| C3×#64685 | 2 |
| #11745850 | 2 |
| #10602043 | 3 |
| #68375 | 5 |