Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
684 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 98 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. #11756863 | C2 | semidirect |
| 3. #11752008 | C2 | semidirect |
| 4. #11752000 | C2 | semidirect |
| 5. #11752000 | C2 | semidirect |
| 6. #11746738 | C2 | semidirect |
| 7. C3×#64867 | C2 | semidirect |
| 39. #64867 | D3 | semidirect |
| 66. C2×C3⋊#170 | D4 | semidirect |
| 72. C2×C3×#170 | D4 | semidirect |
| 217. C2×#170 | D12 | semidirect |
| 493. C3×C5 | #1891 | semidirect |
| 574. C5 | #69036 | semidirect |
| 599. C3 | #10604463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11756863 | 2 |
| #11752871 | 2 |
| #11752008 | 2 |
| #11752000 | 2 |
| #11746738 | 2 |
| C3×#64867 | 2 |
| #10604463 | 3 |
| #69036 | 5 |