Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
432 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 148 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. #10603846 | C3 | direct (N × H) |
| 9. C3×C4×C5×C8 | C4 | semidirect |
| 10. C3×C8×Dic5 | C4 | semidirect |
| 11. C3×C4×#168 | C4 | semidirect |
| 33. C4×C5×C8 | C3×C4 | semidirect |
| 34. C8×Dic5 | C3×C4 | semidirect |
| 35. C4×#168 | C3×C4 | semidirect |
| 53. C3×C4×C8 | AGL(1,𝔽5) | semidirect |
| 102. C4×C8 | C3×AGL(1,𝔽5) | semidirect |
| 136. C3×C5 | #1835 | semidirect |
| 162. C5 | C3×#1835 | semidirect |
| 171. C3 | #10603846 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65689 | 2 |
| C3×C4×C8×D5 | 2 |
| C3×#64893 | 2 |
| #10603846 | 3 |
| C3×#1835 | 5 |