Finite Group DatabasebetaFinite Group DatabasebetaOrder 720.
168 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 52 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. C3×Dic30 | C2 | semidirect |
| 3. C3×C5×Dic6 | C2 | semidirect |
| 4. #67153 | C2 | semidirect |
| 20. Dic30 | D3 | semidirect |
| 21. C5×Dic6 | D3 | semidirect |
| 26. C3⋊D15 | Q8 | semidirect |
| 30. C3×Dic6 | D5 | semidirect |
| 48. C32×C5 | C2×Q8 | semidirect |
| 75. Dic6 | D15 | semidirect |
| 85. C3×C5 | D3×Q8 | semidirect |
| 86. C3×C5 | D3×Q8 | semidirect |
| 102. C32 | Q8×D5 | semidirect |
| 114. C5 | #3797 | semidirect |
| 121. C3 | D15⋊Q8 | semidirect |
| 122. C3 | Q8×D15 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊D15 | 2 |
| C3×Dic30 | 2 |
| C3×C5×Dic6 | 2 |
| #67153 | 2 |
| #67149 | 2 |
| Q8×D15 | 3 |
| D15⋊Q8 | 3 |
| #3797 | 5 |