Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
318 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 178 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×Dic15 | C3 | direct (N × H) |
| 6. C32×C5×Q8 | C4 | semidirect |
| 21. C3×Dic15 | Q8 | direct (N × H) |
| 27. C3×C5×Q8 | Dic3 | semidirect |
| 28. C3×C5×Q8 | C3×C4 | semidirect |
| 44. C32×Q8 | Dic5 | semidirect |
| 55. Dic15 | C3×Q8 | direct (N × H) |
| 65. C32×C5 | C4×Q8 | semidirect |
| 66. C5×Q8 | C3×Dic3 | semidirect |
| 85. C3×Q8 | C3×Dic5 | semidirect |
| 86. C3×Q8 | Dic15 | direct (N × H) |
| 105. C3×C5 | Q8×Dic3 | semidirect |
| 106. C3×C5 | C3×C4×Q8 | semidirect |
| 120. C32 | Q8×Dic5 | semidirect |
| 121. Q8 | C3×Dic15 | direct (N × H) |
| 134. C5 | C3×Q8×Dic3 | semidirect |
| 140. C3 | C3×Q8×Dic5 | semidirect |
| 141. C3 | Q8×Dic15 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×Q8 | 2 |
| C3×C4⋊Dic15 | 2 |
| C3×C4×Dic15 | 2 |
| Q8×Dic15 | 3 |
| C3×Q8×Dic5 | 3 |
| C3×Q8×Dic3 | 5 |