Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
205 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 2. C3⋊#859 | C2 | semidirect |
| 3. C3×#859 | C2 | semidirect |
| 8. D3×SL(2,𝔽3) | C4 | semidirect |
| 15. #859 | D3 | direct (N × H) |
| 23. C3×SL(2,𝔽3) | C2×C4 | semidirect |
| 29. D3×Q8 | Dic3 | semidirect |
| 58. C3×Q8 | C2×Dic3 | semidirect |
| 73. SL(2,𝔽3) | C4×D3 | semidirect |
| 114. Q8 | D3×Dic3 | semidirect |
| 134. D3 | #859 | direct (N × H) |
| 146. C3 | C2×#859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×SL(2,𝔽3) | 2 |
| C3⋊#859 | 2 |
| C3×#859 | 2 |
| C2×#859 | 3 |
| D3×#103 | 3 |
| C2×D3×Dic3 | 4 |