Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
258 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×#887 | C2 | semidirect |
| 4. C32×#107 | C2 | semidirect |
| 5. C3×#815 | C2 | semidirect |
| 6. C3×#810 | C2 | semidirect |
| 9. #4889 | C3 | direct (N × H) |
| 21. C3×#204 | C4 | semidirect |
| 27. #887 | C2×C3 | semidirect |
| 29. C3×#107 | D3 | semidirect |
| 30. C3×#107 | C2×C3 | semidirect |
| 34. #815 | C2×C3 | semidirect |
| 35. #810 | C2×C3 | semidirect |
| 48. C3×Dic6 | C2×C4 | semidirect |
| 49. C32×C8 | C2×C4 | semidirect |
| 78. #204 | C3×C4 | semidirect |
| 93. #107 | C3×D3 | semidirect |
| 123. Dic6 | C2×C3×C4 | semidirect |
| 126. C3×C8 | C4×D3 | semidirect |
| 127. C3×C8 | C2×C3×C4 | semidirect |
| 172. C32 | #440 | semidirect |
| 186. C8 | C3×C4×D3 | semidirect |
| 210. C3 | #4889 | direct (N × H) |
| 211. C3 | C3×#440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#204 | 2 |
| C3×#893 | 2 |
| C3×#887 | 2 |
| C32×#107 | 2 |
| C3×#815 | 2 |
| C3×#810 | 2 |
| C3×#809 | 2 |
| C3×#440 | 3 |
| #4889 | 3 |