Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
496 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 80 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. #11751803 | C2 | semidirect |
| 3. #11746798 | C2 | semidirect |
| 4. C3×#64927 | C2 | semidirect |
| 5. #11746505 | C2 | semidirect |
| 16. #91231 | C22 | semidirect |
| 17. C3×#4002 | C22 | semidirect |
| 25. #64927 | D3 | semidirect |
| 64. #4002 | C2×D3 | semidirect |
| 259. C3×C5 | #1533 | semidirect |
| 306. C5 | #68347 | semidirect |
| 321. C3 | #10604961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#4093 | 2 |
| #11751803 | 2 |
| #11746798 | 2 |
| C3×#64927 | 2 |
| #11746505 | 2 |
| #10604961 | 3 |
| #68347 | 5 |