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. C2×C3×#3932 | C2 | semidirect |
| 3. Dic3×Dic20 | C2 | semidirect |
| 4. C2×#90943 | C2 | semidirect |
| 5. #11746330 | C2 | semidirect |
| 6. C5×Dic3⋊C16 | C2 | semidirect |
| 7. #11745892 | C2 | semidirect |
| 24. C2×#3932 | D3 | semidirect |
| 42. C3×Dic20 | D4 | semidirect |
| 56. Dic3⋊C16 | D5 | semidirect |
| 114. Dic20 | #67 | semidirect |
| 141. C5×Dic3 | SD32 | semidirect |
| 249. C3×C5 | #2207 | semidirect |
| 262. Dic3 | #3932 | semidirect |
| 291. C5 | #71475 | semidirect |
| 305. C3 | #10600085 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3932 | 2 |
| #11748005 | 2 |
| Dic3×Dic20 | 2 |
| C2×#90943 | 2 |
| #11746330 | 2 |
| C5×Dic3⋊C16 | 2 |
| #11745892 | 2 |
| #10600085 | 3 |
| #71475 | 5 |