Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 84 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×#65162 | C2 | semidirect |
| 3. C2×#90943 | C2 | semidirect |
| 4. C2×#90941 | C2 | semidirect |
| 5. #11746312 | C2 | semidirect |
| 6. C5×#4491 | C2 | semidirect |
| 7. #11745927 | C2 | semidirect |
| 26. #65162 | D3 | semidirect |
| 46. C3×Dic20 | D4 | semidirect |
| 55. #4491 | D5 | semidirect |
| 117. Dic20 | D12 | semidirect |
| 141. C3×Dic5 | SD32 | semidirect |
| 228. Dic5 | #828 | semidirect |
| 249. C3×C5 | #2207 | semidirect |
| 291. C5 | #70914 | semidirect |
| 305. C3 | #10599997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65162 | 2 |
| #11747996 | 2 |
| C2×#90943 | 2 |
| C2×#90941 | 2 |
| #11746312 | 2 |
| C5×#4491 | 2 |
| #11745927 | 2 |
| #10599997 | 3 |
| #70914 | 5 |