Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 6. C2×C3×C5×M16 | C4 | semidirect |
| 7. C22×C3×C5×C8 | C4 | semidirect |
| 12. #91120 | C4 | semidirect |
| 43. C2×C5×M16 | Dic3 | semidirect |
| 44. C22×C5×C8 | Dic3 | semidirect |
| 76. C2×C3×M16 | Dic5 | semidirect |
| 77. C22×C3×C8 | Dic5 | semidirect |
| 163. C2×M16 | Dic15 | semidirect |
| 164. C22×C8 | Dic15 | semidirect |
| 230. C3×C5 | #1395 | semidirect |
| 275. C5 | #67692 | semidirect |
| 289. C3 | #10598183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#408 | 2 |
| #11751341 | 2 |
| #11751338 | 2 |
| #10598183 | 3 |
| #67692 | 5 |