Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
334 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 100 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. C3×C4×ΓL(1,𝔽16) | C2 | semidirect |
| 3. C32×C4×AGL(1,𝔽5) | C2 | semidirect |
| 4. C3×Dic3⋊AGL(1,𝔽5) | C2 | semidirect |
| 7. #91909 | C3 | direct (N × H) |
| 11. C3×C4×D15 | C4 | semidirect |
| 12. C3×C4×C5×D3 | C4 | semidirect |
| 14. C3×#1200 | C4 | semidirect |
| 15. C3×D3×Dic5 | C4 | semidirect |
| 20. C4×ΓL(1,𝔽16) | C2×C3 | semidirect |
| 25. C3×C4×AGL(1,𝔽5) | D3 | semidirect |
| 26. C3×C4×AGL(1,𝔽5) | C2×C3 | semidirect |
| 27. Dic3⋊AGL(1,𝔽5) | C2×C3 | semidirect |
| 53. C4×D15 | C3×C4 | semidirect |
| 54. C4×C5×D3 | C3×C4 | semidirect |
| 62. #1200 | C3×C4 | semidirect |
| 63. D3×Dic5 | C3×C4 | semidirect |
| 75. C4×AGL(1,𝔽5) | C3×D3 | semidirect |
| 84. C3×C4×D3 | AGL(1,𝔽5) | semidirect |
| 120. C32×C5 | #117 | semidirect |
| 170. C4×D3 | C3×AGL(1,𝔽5) | semidirect |
| 191. C3×C5 | #872 | semidirect |
| 192. C3×C5 | C3×#117 | semidirect |
| 221. C32 | #4130 | semidirect |
| 241. C5 | C3×#872 | semidirect |
| 253. C3 | #91909 | direct (N × H) |
| 254. C3 | C3×#4130 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D3×D5 | 2 |
| C3×C4×ΓL(1,𝔽16) | 2 |
| C32×C4×AGL(1,𝔽5) | 2 |
| C3×Dic3⋊AGL(1,𝔽5) | 2 |
| C3×(C2×D3)⋊AGL(1,𝔽5) | 2 |
| C3×#4130 | 3 |
| #91909 | 3 |
| C3×#872 | 5 |