Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
330 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 8. C32×Q16 | C4 | semidirect |
| 31. C3×Q16 | Dic3 | semidirect |
| 44. C3⋊Dic3 | Q16 | direct (N × H) |
| 63. Q16 | C3⋊Dic3 | direct (N × H) |
| 77. C32 | C4×Q16 | semidirect |
| 97. C3 | Dic3×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 |
| Q8×C3⋊Dic3 | 2 |
| #63662 | 2 |
| #63645 | 2 |
| C8×C3⋊Dic3 | 2 |
| Dic3×Q16 | 3 |