Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
226 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 36. C3×Dic6 | Q8 | semidirect |
| 96. Dic6 | Dic6 | semidirect |
| 133. C32 | #475 | semidirect |
| 162. C3 | #4851 | semidirect |
| 163. C3 | #5020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64078 | 2 |
| C3×C4×Dic6 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| #63573 | 2 |
| #63566 | 2 |
| #5020 | 3 |
| #4851 | 3 |