Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
720 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#91237 | C2 | semidirect |
| 3. C42×ΓL(1,𝔽16) | C2 | semidirect |
| 4. #11752340 | C2 | semidirect |
| 10. C3×C5×#127 | C4 | semidirect |
| 12. C3×#4082 | C4 | semidirect |
| 15. C3×#4015 | C4 | semidirect |
| 36. C4×ΓL(1,𝔽16) | D4 | semidirect |
| 51. C5×#127 | Dic3 | semidirect |
| 53. #4082 | Dic3 | semidirect |
| 56. #4015 | Dic3 | semidirect |
| 81. C3×#127 | AGL(1,𝔽5) | semidirect |
| 121. C3×C4×C5 | #104 | semidirect |
| 169. #127 | ΓL(1,𝔽16) | semidirect |
| 207. C4×C5 | #837 | semidirect |
| 233. C3×C5 | #1962 | semidirect |
| 243. C3×C4 | #4008 | semidirect |
| 273. C5 | #71815 | semidirect |
| 284. C4 | #91237 | semidirect |
| 286. C3 | #10604611 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66050 | 2 |
| C2×#91237 | 2 |
| C42×ΓL(1,𝔽16) | 2 |
| #11752340 | 2 |
| #10604611 | 3 |
| #71815 | 5 |