Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. C2×C32×C5×Q8 | C2 | semidirect |
| 3. #10623908 | C2 | semidirect |
| 4. C4×C3⋊Dic15 | C2 | semidirect |
| 13. C2×C3×C5×Q8 | D3 | semidirect |
| 24. C2×C32×Q8 | D5 | semidirect |
| 38. C2×C5×Q8 | C3⋊D3 | semidirect |
| 54. C2×C3×Q8 | D15 | semidirect |
| 58. C32×C5 | #124 | semidirect |
| 90. C2×Q8 | C3⋊D15 | semidirect |
| 94. C3×C5 | #947 | semidirect |
| 104. C32 | #4093 | semidirect |
| 114. C5 | #64156 | semidirect |
| 121. C3 | #91836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×Q8 | 2 |
| C2×C4⋊(C3⋊D15) | 2 |
| #10623908 | 2 |
| C4×C3⋊Dic15 | 2 |
| #91836 | 3 |
| #64156 | 5 |