Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
140 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 3. #10598646 | C3 | direct (N × H) |
| 15. C3×C5×C16 | C8 | semidirect |
| 39. C5×C16 | C3×C8 | semidirect |
| 53. C3×C16 | #170 | semidirect |
| 85. C16 | C3×#170 | semidirect |
| 86. C3×C5 | #1372 | semidirect |
| 105. C5 | C3×#1372 | semidirect |
| 111. C3 | #10598646 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64882 | 2 |
| C3×C16×Dic5 | 2 |
| #10598646 | 3 |
| C3×#1372 | 5 |