Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 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. C3×C4×ΓL(1,𝔽16) | C2 | semidirect |
| 4. ΓL(1,𝔽16)⋊Dic3 | C2 | semidirect |
| 8. ΓL(1,𝔽16)⋊D3 | C4 | direct (N × H) |
| 9. C4×C3⋊D15 | C4 | semidirect |
| 10. C4×C5×C3⋊D3 | C4 | semidirect |
| 12. #67137 | C4 | semidirect |
| 13. C3⋊D3×Dic5 | C4 | semidirect |
| 19. C4×ΓL(1,𝔽16) | D3 | semidirect |
| 26. C3×ΓL(1,𝔽16) | C2×C4 | semidirect |
| 27. C32×C4×C5 | C2×C4 | semidirect |
| 28. C3⋊Dic15 | C2×C4 | semidirect |
| 29. C5×C3⋊Dic3 | C2×C4 | semidirect |
| 30. C32×Dic5 | C2×C4 | semidirect |
| 55. C3⋊D15 | C42 | semidirect |
| 56. C5×C3⋊D3 | C42 | semidirect |
| 68. C4×C3⋊D3 | AGL(1,𝔽5) | semidirect |
| 79. ΓL(1,𝔽16) | C4×D3 | semidirect |
| 82. C3×C4×C5 | C4×D3 | semidirect |
| 86. C3×Dic5 | C4×D3 | semidirect |
| 95. C32×C5 | C2×C42 | semidirect |
| 110. C32×C4 | C2×AGL(1,𝔽5) | semidirect |
| 112. C3⋊Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 146. C4×C5 | #624 | semidirect |
| 148. Dic5 | #624 | semidirect |
| 152. C3⋊D3 | C4×AGL(1,𝔽5) | semidirect |
| 158. C3×C5 | C42×D3 | semidirect |
| 171. C3×C4 | D3×AGL(1,𝔽5) | semidirect |
| 181. C32 | C2×C4×AGL(1,𝔽5) | semidirect |
| 199. C5 | C4×#624 | semidirect |
| 208. C4 | ΓL(1,𝔽16)⋊D3 | direct (N × H) |
| 210. C3 | C4×D3×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×ΓL(1,𝔽16)⋊D3 | 2 |
| C4×D5×C3⋊D3 | 2 |
| C3×C4×ΓL(1,𝔽16) | 2 |
| ΓL(1,𝔽16)⋊Dic3 | 2 |
| C4×D3×AGL(1,𝔽5) | 3 |
| C4×#624 | 5 |