Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
236 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 236 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 |
|---|---|---|
| 7. #4716 | C3 | direct (N × H) |
| 15. C3×Dic12 | C4 | semidirect |
| 54. Dic12 | C3×C4 | semidirect |
| 112. C32 | #441 | semidirect |
| 134. C3 | #4716 | direct (N × H) |
| 135. C3 | C3×#441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C3×C4×Dic6 | 2 |
| C32×#97 | 2 |
| C3×#817 | 2 |
| C3×#816 | 2 |
| C3×#441 | 3 |
| #4716 | 3 |