Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
464 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 4. #11746741 | C2 | semidirect |
| 5. C3×#64870 | C2 | semidirect |
| 6. #11746507 | C2 | semidirect |
| 7. #11746506 | C2 | semidirect |
| 35. #64870 | D3 | direct (N × H) |
| 252. C5×D3 | #330 | semidirect |
| 316. C3×C5 | C2×#330 | semidirect |
| 358. D3 | #64870 | direct (N × H) |
| 359. C5 | D3×#330 | semidirect |
| 374. C3 | C2×#64870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#4036 | 2 |
| D3×#4002 | 2 |
| #11746741 | 2 |
| C3×#64870 | 2 |
| #11746507 | 2 |
| #11746506 | 2 |
| C2×#64870 | 3 |
| D3×#330 | 5 |