Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
250 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 118 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. Dic3×Q16 | C3 | direct (N × H) |
| 9. C32×Q16 | C4 | semidirect |
| 41. C3×Q16 | Dic3 | direct (N × H) |
| 42. C3×Q16 | C3×C4 | semidirect |
| 62. C3×Dic3 | Q16 | direct (N × H) |
| 95. Q16 | C3×Dic3 | direct (N × H) |
| 119. Dic3 | C3×Q16 | direct (N × H) |
| 120. C32 | C4×Q16 | semidirect |
| 147. C3 | Dic3×Q16 | direct (N × H) |
| 148. C3 | C3×C4×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q16 | 2 |
| C3×Q8×Dic3 | 2 |
| C3×#835 | 2 |
| C3×#818 | 2 |
| C3×C8×Dic3 | 2 |
| C3×C4×Q16 | 3 |
| Dic3×Q16 | 3 |