Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
459 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 459 conjugacy classes of subgroups — too many to draw. Only its 246 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 |
|---|---|---|
| 7. Q8×Dic6 | C3 | direct (N × H) |
| 28. C32×Q8 | Q8 | semidirect |
| 35. C3×Dic6 | Q8 | direct (N × H) |
| 72. C3×Q8 | Dic6 | direct (N × H) |
| 73. C3×Q8 | C3×Q8 | semidirect |
| 88. Dic6 | C3×Q8 | direct (N × H) |
| 117. C32 | Q82 | semidirect |
| 120. Q8 | C3×Dic6 | direct (N × H) |
| 142. C3 | Q8×Dic6 | direct (N × H) |
| 143. C3 | C3×Q82 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q8 | 2 |
| C3×Q8×Dic3 | 2 |
| C3×#888 | 2 |
| C3×#869 | 2 |
| C3×C4×Dic6 | 2 |
| C3×Q82 | 3 |
| Q8×Dic6 | 3 |