Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
268 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 1. C2×C3×Dic12 | C2 | semidirect |
| 3. #63873 | C2 | semidirect |
| 5. C2×#3718 | C2 | semidirect |
| 7. #63642 | C2 | semidirect |
| 33. C2×Dic12 | D3 | semidirect |
| 174. C32 | #497 | semidirect |
| 209. C3 | #5167 | semidirect |
| 210. C3 | #5190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C2×C3×#204 | 2 |
| #63873 | 2 |
| #63863 | 2 |
| C2×#3718 | 2 |
| C2×#3715 | 2 |
| #63642 | 2 |
| #5190 | 3 |
| #5167 | 3 |