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×Q8 | C4 | semidirect |
| 8. C32×D20 | C4 | semidirect |
| 27. C3×C5×Q8 | Dic3 | semidirect |
| 29. C3×D20 | Dic3 | semidirect |
| 40. C32×Q8 | AGL(1,𝔽5) | semidirect |
| 56. C32×C5 | #104 | semidirect |
| 58. C5×Q8 | C3⋊Dic3 | semidirect |
| 60. D20 | C3⋊Dic3 | semidirect |
| 74. C3×Q8 | ΓL(1,𝔽16) | semidirect |
| 93. C3×C5 | #837 | semidirect |
| 103. C32 | #4010 | semidirect |
| 104. Q8 | C3⋊ΓL(1,𝔽16) | semidirect |
| 114. C5 | #63664 | semidirect |
| 121. C3 | #91239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#713 | 2 |
| C4×C3⋊ΓL(1,𝔽16) | 2 |
| #10624093 | 2 |
| #91239 | 3 |
| #63664 | 5 |