Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 336 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 |
|---|---|---|
| 1. C3×#65788 | C2 | semidirect |
| 4. #11746801 | C2 | semidirect |
| 5. #11746512 | C2 | semidirect |
| 7. #170⋊(C3⋊C8) | C2 | semidirect |
| 25. #65788 | D3 | semidirect |
| 90. C3×#170 | SD16 | semidirect |
| 180. #170 | #215 | semidirect |
| 252. C3×C5 | #1582 | semidirect |
| 293. C5 | #70953 | semidirect |
| 306. C3 | #10603971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65788 | 2 |
| #11751893 | 2 |
| #11749221 | 2 |
| #11746801 | 2 |
| #11746512 | 2 |
| #11746490 | 2 |
| #170⋊(C3⋊C8) | 2 |
| #10603971 | 3 |
| #70953 | 5 |