Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 2. #11746724 | C2 | semidirect |
| 5. C3×#4020 | C4 | semidirect |
| 8. C3×C4×C5×C8 | C4 | semidirect |
| 23. #4020 | Dic3 | semidirect |
| 26. C4×C5×C8 | Dic3 | semidirect |
| 41. C3×C4×C8 | AGL(1,𝔽5) | semidirect |
| 83. C4×C8 | ΓL(1,𝔽16) | semidirect |
| 114. C3×C5 | #1408 | semidirect |
| 141. C5 | #67792 | semidirect |
| 150. C3 | #10598516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64984 | 2 |
| #11746724 | 2 |
| #10598516 | 3 |
| #67792 | 5 |