Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
266 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 1. C32×C5×C4⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic15 | C2 | semidirect |
| 6. C3×#6712 | C2 | semidirect |
| 7. C3×C4×Dic15 | C2 | semidirect |
| 8. #91787 | C3 | direct (N × H) |
| 19. C3×C5×C4⋊C4 | D3 | semidirect |
| 20. C3×C5×C4⋊C4 | C2×C3 | semidirect |
| 24. C4⋊Dic15 | C2×C3 | semidirect |
| 25. #6712 | C2×C3 | semidirect |
| 26. C4×Dic15 | C2×C3 | semidirect |
| 44. C32×C4⋊C4 | D5 | semidirect |
| 74. C5×C4⋊C4 | C3×D3 | semidirect |
| 115. C3×C4⋊C4 | C3×D5 | semidirect |
| 116. C3×C4⋊C4 | D15 | semidirect |
| 127. C32×C5 | #126 | semidirect |
| 190. C4⋊C4 | C3×D15 | semidirect |
| 196. C3×C5 | #898 | semidirect |
| 197. C3×C5 | C3×#126 | semidirect |
| 226. C32 | #4044 | semidirect |
| 245. C5 | C3×#898 | semidirect |
| 257. C3 | C3×#4044 | semidirect |
| 258. C3 | #91787 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×C4⋊C4 | 2 |
| C3×#6714 | 2 |
| C3×C4⋊Dic15 | 2 |
| C3×#6712 | 2 |
| C3×C4×Dic15 | 2 |
| #91787 | 3 |
| C3×#4044 | 3 |
| C3×#898 | 5 |