Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
314 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 7. #4985 | C3 | direct (N × H) |
| 142. C32 | #400 | semidirect |
| 182. C3 | #4985 | direct (N × H) |
| 183. C3 | C3×#400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4⋊C4 | 2 |
| C2×C3×Dic3⋊C4 | 2 |
| C3×C3⋊#95 | 2 |
| C3×#400 | 3 |
| #4985 | 3 |