Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
264 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 81 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. C4×C3⋊ΓL(1,𝔽16) | C2 | semidirect |
| 3. #10624093 | C2 | semidirect |
| 6. C32×C5×D4 | C4 | semidirect |
| 10. C32×Dic10 | C4 | semidirect |
| 27. C3×C5×D4 | Dic3 | semidirect |
| 31. C3×Dic10 | Dic3 | semidirect |
| 42. C32×D4 | AGL(1,𝔽5) | semidirect |
| 56. C32×C5 | #104 | semidirect |
| 58. C5×D4 | C3⋊Dic3 | semidirect |
| 62. Dic10 | C3⋊Dic3 | semidirect |
| 76. C3×D4 | ΓL(1,𝔽16) | semidirect |
| 93. C3×C5 | #837 | semidirect |
| 103. C32 | #4008 | semidirect |
| 106. D4 | C3⋊ΓL(1,𝔽16) | semidirect |
| 114. C5 | #63664 | semidirect |
| 121. C3 | #91237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#711 | 2 |
| C4×C3⋊ΓL(1,𝔽16) | 2 |
| #10624093 | 2 |
| #91237 | 3 |
| #63664 | 5 |