Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
214 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 5. #4558 | C3 | direct (N × H) |
| 135. C32 | #341 | semidirect |
| 167. C3 | #4558 | direct (N × H) |
| 168. C3 | C3×#341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×M16 | 2 |
| C2×C3×#208 | 2 |
| C22×C3×C3⋊C8 | 2 |
| C3×#341 | 3 |
| #4558 | 3 |