Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
312 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 107 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. #63662 | C2 | semidirect |
| 5. #63635 | C2 | semidirect |
| 87. C32 | #483 | semidirect |
| 111. C3 | #5043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C22⋊Q8 | 2 |
| C2×C4⋊(C3⋊Dic3) | 2 |
| #63662 | 2 |
| #63657 | 2 |
| #63635 | 2 |
| #5043 | 3 |