Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
486 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 147 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. ΓL(1,𝔽16)⋊Dic3 | C2 | direct (N × H) |
| 6. C2×C3×ΓL(1,𝔽16) | C4 | semidirect |
| 8. C2×C3⋊Dic15 | C4 | semidirect |
| 9. C2×C5×C3⋊Dic3 | C4 | semidirect |
| 10. D5×C3⋊Dic3 | C4 | semidirect |
| 22. C3×ΓL(1,𝔽16) | C2×C4 | semidirect |
| 23. C3⋊Dic15 | C2×C4 | semidirect |
| 24. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 31. C2×ΓL(1,𝔽16) | Dic3 | semidirect |
| 44. C2×C32×C5 | C42 | semidirect |
| 46. C32×D5 | C42 | semidirect |
| 55. C2×C3⋊Dic3 | AGL(1,𝔽5) | semidirect |
| 67. ΓL(1,𝔽16) | C2×Dic3 | semidirect |
| 78. C32×C5 | C2×C42 | semidirect |
| 91. C3⋊Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 96. C2×C3×C5 | C4×Dic3 | semidirect |
| 100. C3×D5 | C4×Dic3 | semidirect |
| 126. C2×C32 | C4×AGL(1,𝔽5) | semidirect |
| 132. C3×C5 | C2×C4×Dic3 | semidirect |
| 148. C2×C5 | Dic32 | semidirect |
| 150. D5 | Dic32 | semidirect |
| 152. C32 | C2×C4×AGL(1,𝔽5) | semidirect |
| 167. C2×C3 | Dic3×AGL(1,𝔽5) | semidirect |
| 169. C5 | C2×Dic32 | semidirect |
| 178. C3 | C2×Dic3×AGL(1,𝔽5) | semidirect |
| 181. C2 | ΓL(1,𝔽16)⋊Dic3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×ΓL(1,𝔽16) | 2 |
| C2×D5×C3⋊Dic3 | 2 |
| ΓL(1,𝔽16)⋊Dic3 | 2 |
| C2×Dic3×AGL(1,𝔽5) | 3 |
| C2×Dic32 | 5 |