Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
500 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 96 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. #11751171 | C2 | semidirect |
| 3. #11747101 | C2 | semidirect |
| 4. #11746964 | C2 | semidirect |
| 5. C3×#64764 | C2 | semidirect |
| 6. #11745842 | C2 | semidirect |
| 7. #11745836 | C2 | semidirect |
| 31. #64764 | D3 | semidirect |
| 321. C3×C5 | #1641 | semidirect |
| 376. C5 | #68407 | semidirect |
| 393. C3 | #10602713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5718 | 2 |
| #11751171 | 2 |
| #11747101 | 2 |
| #11746964 | 2 |
| C3×#64764 | 2 |
| #11745842 | 2 |
| #11745836 | 2 |
| #10602713 | 3 |
| #68407 | 5 |