Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
190 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 86 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. #4878 | C3 | direct (N × H) |
| 107. C32 | #499 | semidirect |
| 132. C3 | #4878 | direct (N × H) |
| 133. C3 | C3×#499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#890 | 2 |
| C32×#107 | 2 |
| C3×#818 | 2 |
| C3×C8×Dic3 | 2 |
| C3×#808 | 2 |
| C3×#499 | 3 |
| #4878 | 3 |