Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
306 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 108 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. #63572 | C2 | semidirect |
| 48. C3⋊Dic3 | M16 | semidirect |
| 96. C32 | #423 | semidirect |
| 121. C3 | #5118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊Dic3 | 2 |
| C2×C3×#208 | 2 |
| #63572 | 2 |
| #5118 | 3 |