Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
318 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 318 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 |
|---|---|---|
| 4. Q8×ΓL(1,𝔽16) | C3 | direct (N × H) |
| 8. C32×C5×Q8 | C4 | semidirect |
| 10. C32×Dic10 | C4 | semidirect |
| 21. C3×ΓL(1,𝔽16) | Q8 | direct (N × H) |
| 33. C3×C5×Q8 | Dic3 | semidirect |
| 34. C3×C5×Q8 | C3×C4 | semidirect |
| 39. C3×Dic10 | Dic3 | semidirect |
| 40. C3×Dic10 | C3×C4 | semidirect |
| 50. C32×Q8 | AGL(1,𝔽5) | semidirect |
| 58. ΓL(1,𝔽16) | C3×Q8 | direct (N × H) |
| 74. C32×C5 | C4×Q8 | semidirect |
| 77. C5×Q8 | C3×Dic3 | semidirect |
| 79. Dic10 | C3×Dic3 | semidirect |
| 99. C3×Q8 | C3×AGL(1,𝔽5) | semidirect |
| 100. C3×Q8 | ΓL(1,𝔽16) | direct (N × H) |
| 120. C3×C5 | Q8×Dic3 | semidirect |
| 121. C3×C5 | C3×C4×Q8 | semidirect |
| 138. C32 | Q8×AGL(1,𝔽5) | semidirect |
| 140. Q8 | C3×ΓL(1,𝔽16) | direct (N × H) |
| 153. C5 | C3×Q8×Dic3 | semidirect |
| 160. C3 | C3×Q8×AGL(1,𝔽5) | semidirect |
| 161. C3 | Q8×ΓL(1,𝔽16) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×D5 | 2 |
| C3×C4⋊ΓL(1,𝔽16) | 2 |
| C3×C4×ΓL(1,𝔽16) | 2 |
| Q8×ΓL(1,𝔽16) | 3 |
| C3×Q8×AGL(1,𝔽5) | 3 |
| C3×Q8×Dic3 | 5 |