Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
|---|---|---|
| 20. C32×C4×C5 | Q8 | semidirect |
| 22. C3⋊Dic15 | Q8 | semidirect |
| 53. C3×C4×C5 | Dic6 | semidirect |
| 63. C32×C5 | C4⋊Q8 | semidirect |
| 72. C32×C4 | Dic10 | semidirect |
| 88. C4×C5 | #634 | semidirect |
| 100. C3×C5 | #888 | semidirect |
| 103. C3×C4 | #1204 | semidirect |
| 110. C32 | #4034 | semidirect |
| 120. C5 | #64097 | semidirect |
| 126. C4 | #67141 | semidirect |
| 127. C3 | #91470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67141 | 2 |
| C4×C3⋊Dic15 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C32×C4⋊Dic5 | 2 |
| #10623774 | 2 |
| #91470 | 3 |
| #64097 | 5 |