Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
260 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #63843 | C2 | semidirect |
| 4. #63642 | C2 | semidirect |
| 5. C3×#818 | C2 | semidirect |
| 6. #63565 | C2 | semidirect |
| 18. C3×#204 | C4 | semidirect |
| 31. #818 | D3 | semidirect |
| 47. C3×Dic6 | C2×C4 | semidirect |
| 49. C32×C8 | C2×C4 | semidirect |
| 78. #204 | Dic3 | semidirect |
| 123. Dic6 | C2×Dic3 | semidirect |
| 125. C3×C8 | C4×D3 | semidirect |
| 126. C3×C8 | C2×Dic3 | semidirect |
| 173. C32 | #440 | semidirect |
| 187. C8 | D3×Dic3 | semidirect |
| 211. C3 | #4889 | semidirect |
| 212. C3 | #5164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#204 | 2 |
| #63898 | 2 |
| #63843 | 2 |
| #63642 | 2 |
| C3×#818 | 2 |
| #63565 | 2 |
| #63562 | 2 |
| #5164 | 3 |
| #4889 | 3 |