Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
336 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 112 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. #10598526 | C3 | direct (N × H) |
| 11. C3×C4×#170 | C4 | semidirect |
| 12. C3×C4×C5×C8 | C4 | semidirect |
| 15. C3×C4×#168 | C4 | semidirect |
| 26. C3×C4×AGL(1,𝔽5) | C8 | semidirect |
| 42. C4×#170 | C3×C4 | semidirect |
| 43. C4×C5×C8 | C3×C4 | semidirect |
| 46. C4×#168 | C3×C4 | semidirect |
| 73. C3×C4×C8 | AGL(1,𝔽5) | semidirect |
| 82. C4×AGL(1,𝔽5) | C3×C8 | semidirect |
| 142. C4×C8 | C3×AGL(1,𝔽5) | semidirect |
| 191. C3×C5 | #1274 | semidirect |
| 229. C5 | C3×#1274 | semidirect |
| 242. C3 | #10598526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65686 | 2 |
| C3×#65678 | 2 |
| C3×#64974 | 2 |
| #10598526 | 3 |
| C3×#1274 | 5 |