Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
208 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 4. #10598271 | C3 | direct (N × H) |
| 5. C2×C3×C5×Q16 | C4 | semidirect |
| 9. C3×C5×#106 | C4 | semidirect |
| 32. C2×C5×Q16 | C3×C4 | semidirect |
| 36. C5×#106 | C3×C4 | semidirect |
| 52. C2×C3×Q16 | Dic5 | semidirect |
| 57. C3×#106 | Dic5 | semidirect |
| 109. C2×Q16 | C3×Dic5 | semidirect |
| 114. #106 | C3×Dic5 | semidirect |
| 153. C3×C5 | #1340 | semidirect |
| 181. C5 | C3×#1340 | semidirect |
| 191. C3 | #10598271 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×#470 | 2 |
| C3×#64777 | 2 |
| C3×#64773 | 2 |
| #10598271 | 3 |
| C3×#1340 | 5 |