Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
362 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 174 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. #4936 | C3 | direct (N × H) |
| 9. C32×C42 | C4 | semidirect |
| 37. C3×C42 | Dic3 | semidirect |
| 38. C3×C42 | C3×C4 | semidirect |
| 80. C42 | C3×Dic3 | semidirect |
| 101. C32 | #382 | semidirect |
| 130. C3 | #4936 | direct (N × H) |
| 131. C3 | C3×#382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C42 | 2 |
| C2×C3×C4⋊Dic3 | 2 |
| C3×C3⋊#95 | 2 |
| C3×#382 | 3 |
| #4936 | 3 |