Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
462 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 126 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. C4×C3⋊ΓL(1,𝔽16) | C2 | semidirect |
| 4. C3×C4×ΓL(1,𝔽16) | C2 | semidirect |
| 5. Dic3×ΓL(1,𝔽16) | C2 | semidirect |
| 11. D3×ΓL(1,𝔽16) | C4 | direct (N × H) |
| 12. C3×C4×D15 | C4 | semidirect |
| 13. C3×C4×C5×D3 | C4 | semidirect |
| 15. C3×#1200 | C4 | semidirect |
| 16. C3×D3×Dic5 | C4 | semidirect |
| 27. C4×ΓL(1,𝔽16) | D3 | direct (N × H) |
| 34. C3⋊ΓL(1,𝔽16) | C2×C4 | semidirect |
| 35. C3×ΓL(1,𝔽16) | C2×C4 | semidirect |
| 36. C32×C4×C5 | C2×C4 | semidirect |
| 37. C3×Dic15 | C2×C4 | semidirect |
| 38. C3×C5×Dic3 | C2×C4 | semidirect |
| 39. C32×Dic5 | C2×C4 | semidirect |
| 56. C4×D15 | Dic3 | semidirect |
| 57. C4×C5×D3 | Dic3 | semidirect |
| 65. #1200 | Dic3 | semidirect |
| 66. D3×Dic5 | Dic3 | semidirect |
| 71. C3×D15 | C42 | semidirect |
| 72. C3×C5×D3 | C42 | semidirect |
| 87. C3×C4×D3 | AGL(1,𝔽5) | semidirect |
| 101. ΓL(1,𝔽16) | C4×D3 | direct (N × H) |
| 105. C3×C4×C5 | C4×D3 | semidirect |
| 106. C3×C4×C5 | C2×Dic3 | semidirect |
| 107. Dic15 | C2×Dic3 | semidirect |
| 110. C3×Dic5 | C4×D3 | semidirect |
| 111. C3×Dic5 | C2×Dic3 | semidirect |
| 112. C5×Dic3 | C2×Dic3 | semidirect |
| 124. C32×C5 | C2×C42 | semidirect |
| 140. C32×C4 | C2×AGL(1,𝔽5) | semidirect |
| 144. C3×Dic3 | C2×AGL(1,𝔽5) | semidirect |
| 150. D15 | C4×Dic3 | semidirect |
| 155. C5×D3 | C4×Dic3 | semidirect |
| 177. C4×D3 | ΓL(1,𝔽16) | direct (N × H) |
| 185. C4×C5 | D3×Dic3 | semidirect |
| 187. Dic5 | D3×Dic3 | semidirect |
| 191. C3×D3 | C4×AGL(1,𝔽5) | semidirect |
| 198. C3×C5 | C42×D3 | semidirect |
| 199. C3×C5 | C2×C4×Dic3 | semidirect |
| 216. C3×C4 | D3×AGL(1,𝔽5) | semidirect |
| 217. C3×C4 | C2×ΓL(1,𝔽16) | semidirect |
| 223. Dic3 | C2×ΓL(1,𝔽16) | semidirect |
| 228. C32 | C2×C4×AGL(1,𝔽5) | semidirect |
| 248. D3 | C4×ΓL(1,𝔽16) | direct (N × H) |
| 249. C5 | C4×D3×Dic3 | semidirect |
| 259. C4 | D3×ΓL(1,𝔽16) | direct (N × H) |
| 261. C3 | C4×D3×AGL(1,𝔽5) | semidirect |
| 262. C3 | C2×C4×ΓL(1,𝔽16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×ΓL(1,𝔽16) | 2 |
| C3×C4×D3×D5 | 2 |
| C4×C3⋊ΓL(1,𝔽16) | 2 |
| C3×C4×ΓL(1,𝔽16) | 2 |
| Dic3×ΓL(1,𝔽16) | 2 |
| C2×C4×ΓL(1,𝔽16) | 3 |
| C4×D3×AGL(1,𝔽5) | 3 |
| C4×D3×Dic3 | 5 |