Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
348 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 98 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. #11747809 | C2 | semidirect |
| 3. C16×Dic15 | C2 | semidirect |
| 4. C5×#4504 | C2 | semidirect |
| 5. #11745891 | C2 | semidirect |
| 13. C3×D80 | C4 | semidirect |
| 28. C3×D40 | C2×C4 | semidirect |
| 30. C3×C5×C16 | C2×C4 | semidirect |
| 35. #4504 | D5 | semidirect |
| 44. D80 | Dic3 | semidirect |
| 73. D40 | C2×Dic3 | semidirect |
| 74. C5×C16 | C2×Dic3 | semidirect |
| 88. Dic15 | D16 | semidirect |
| 99. C3×C16 | C4×D5 | semidirect |
| 154. C16 | D5×Dic3 | semidirect |
| 155. C3×C5 | C4×D16 | semidirect |
| 184. C5 | Dic3×D16 | semidirect |
| 194. C3 | #10600110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D80 | 2 |
| #11747809 | 2 |
| C16×Dic15 | 2 |
| C5×#4504 | 2 |
| #11745891 | 2 |
| #10600110 | 3 |
| Dic3×D16 | 5 |