Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
735 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 735 conjugacy classes of subgroups — too many to draw. Only its 112 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×Dic3×H(3,𝔽3) | C2 | semidirect |
| 3. C32×#624 | C3 | semidirect |
| 6. C3⋊D3×H(3,𝔽3) | C4 | semidirect |
| 8. C33×Dic3 | C2×C3 | semidirect |
| 13. Dic3×H(3,𝔽3) | D3 | semidirect |
| 14. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 20. C32×C3⋊D3 | C3×C4 | semidirect |
| 35. C32×Dic3 | C3×D3 | semidirect |
| 40. C34 | C2×C3×C4 | semidirect |
| 44. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 48. #624 | H(3,𝔽3) | direct (N × H) |
| 80. C3×Dic3 | C2×H(3,𝔽3) | semidirect |
| 88. C33 | C3×C4×D3 | semidirect |
| 93. H(3,𝔽3) | #624 | direct (N × H) |
| 114. C3⋊D3 | C4×H(3,𝔽3) | semidirect |
| 128. Dic3 | D3×H(3,𝔽3) | semidirect |
| 142. C32 | C2×C4×H(3,𝔽3) | semidirect |
| 143. C32 | C3×#624 | semidirect |
| 166. C3 | C4×D3×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊D3×H(3,𝔽3) | 2 |
| C3×Dic3×H(3,𝔽3) | 2 |
| C32×#624 | 3 |
| C4×D3×H(3,𝔽3) | 3 |