Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
266 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 42. C3⋊Dic3 | Q16 | semidirect |
| 81. C32 | #494 | semidirect |
| 99. C3 | #5183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| #63873 | 2 |
| C2×#3718 | 2 |
| C8×C3⋊Dic3 | 2 |
| #5183 | 3 |