Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
145 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 145 conjugacy classes of subgroups — too many to draw. Only its 19 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. AΓL(1,𝔽16) | C2 | direct (N × H) |
| 4. C2×AGL(1,𝔽16) | C4 | semidirect |
| 5. ((C24⋊C5)⋊C2)⋊C3 | C4 | semidirect |
| 10. AGL(1,𝔽16) | C2×C4 | semidirect |
| 13. C2×C24⋊C5 | Dic3 | semidirect |
| 14. (C24⋊C5)⋊C2 | Dic3 | semidirect |
| 18. C2×C22⋊A4 | AGL(1,𝔽5) | semidirect |
| 22. C24⋊C5 | C2×Dic3 | semidirect |
| 30. C22⋊A4 | C2×AGL(1,𝔽5) | semidirect |
| 34. C25 | ΓL(1,𝔽16) | semidirect |
| 59. C24 | C2×ΓL(1,𝔽16) | semidirect |
| 127. C2 | AΓL(1,𝔽16) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×((C24⋊C5)⋊C2)⋊C3 | 2 |
| AΓL(1,𝔽16) | 2 |
| C2×#66297 | 3 |
| C2×#4625 | 5 |
| C2×ΓL(1,𝔽16) | 16 |