Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 88 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×#65365 | C2 | semidirect |
| 3. #11747008 | C2 | semidirect |
| 4. #11746900 | C2 | semidirect |
| 5. #11746365 | C2 | semidirect |
| 6. #11745867 | C2 | semidirect |
| 7. #11745855 | C2 | semidirect |
| 26. #65365 | D3 | semidirect |
| 96. C3×#168 | D8 | semidirect |
| 196. #168 | #213 | semidirect |
| 274. C3×C5 | #1685 | semidirect |
| 322. C5 | #71268 | semidirect |
| 337. C3 | #10601801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5072 | 2 |
| C3×#65365 | 2 |
| #11747008 | 2 |
| #11746900 | 2 |
| #11746365 | 2 |
| #11745867 | 2 |
| #11745855 | 2 |
| #10601801 | 3 |
| #71268 | 5 |