Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
340 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 78 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. C2×#91112 | C2 | semidirect |
| 2. C5×#5191 | C2 | semidirect |
| 3. #11747793 | C2 | semidirect |
| 5. C3×#64784 | C2 | semidirect |
| 6. Dic3⋊#672 | C2 | semidirect |
| 7. #11745893 | C2 | semidirect |
| 27. #64784 | D3 | semidirect |
| 50. #5191 | D5 | semidirect |
| 246. C3×C5 | #2210 | semidirect |
| 287. C5 | #69235 | semidirect |
| 301. C3 | #10602116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#91112 | 2 |
| C5×#5191 | 2 |
| #11747793 | 2 |
| C2×#90939 | 2 |
| C3×#64784 | 2 |
| Dic3⋊#672 | 2 |
| #11745893 | 2 |
| #10602116 | 3 |
| #69235 | 5 |