Finite Group DatabasebetaFinite Group DatabasebetaOrder 480.
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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 |
|---|---|---|
| 3. #6718 | C2 | semidirect |
| 4. C3×#689 | C2 | semidirect |
| 5. #6663 | C2 | semidirect |
| 6. #6661 | C2 | semidirect |
| 26. #689 | D3 | direct (N × H) |
| 55. C5×D3 | Q16 | semidirect |
| 81. C3×C5 | C2×Q16 | semidirect |
| 103. D3 | #689 | direct (N × H) |
| 104. C5 | D3×Q16 | semidirect |
| 112. C3 | C2×#689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D3×Q8 | 2 |
| D3×Dic10 | 2 |
| #6718 | 2 |
| C3×#689 | 2 |
| #6663 | 2 |
| #6661 | 2 |
| D3×#168 | 2 |
| C2×#689 | 3 |
| D3×Q16 | 5 |