Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
332 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 332 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. #10598790 | C3 | direct (N × H) |
| 6. C2×C3×C5×M16 | C4 | semidirect |
| 7. C22×C3×#168 | C4 | semidirect |
| 8. C3×#4011 | C4 | semidirect |
| 32. C2×C5×M16 | C3×C4 | semidirect |
| 33. C22×#168 | C3×C4 | semidirect |
| 34. #4011 | C3×C4 | semidirect |
| 54. C2×C3×M16 | AGL(1,𝔽5) | semidirect |
| 116. C2×M16 | C3×AGL(1,𝔽5) | semidirect |
| 165. C3×C5 | #1391 | semidirect |
| 199. C5 | C3×#1391 | semidirect |
| 210. C3 | #10598790 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65745 | 2 |
| C3×#65418 | 2 |
| #10598790 | 3 |
| C3×#1391 | 5 |