Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. C22×C3⋊Dic3 | C4 | semidirect |
| 10. C32×C22⋊C4 | C4 | semidirect |
| 14. #3757 | C4 | semidirect |
| 38. C3×C22⋊C4 | Dic3 | semidirect |
| 94. C22⋊C4 | C3⋊Dic3 | semidirect |
| 112. C32 | #342 | semidirect |
| 152. C3 | #4527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C22⋊C4 | 2 |
| C2×#3757 | 2 |
| #4527 | 3 |