Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
492 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 5. C2×C3×C5×M16 | C4 | semidirect |
| 9. #91115 | C4 | semidirect |
| 27. C2×C5×M16 | Dic3 | semidirect |
| 49. C2×C3×M16 | Dic5 | semidirect |
| 105. C2×M16 | Dic15 | semidirect |
| 151. C3×C5 | #1297 | semidirect |
| 186. C5 | #67683 | semidirect |
| 198. C3 | #10598174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#407 | 2 |
| C4×#6719 | 2 |
| #10598174 | 3 |
| #67683 | 5 |