Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
913 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 913 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.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C3⋊#1113 |
| commutator, Fitting, cosocle | C2×C32×H(3,𝔽3) | C22 |
| socle | C2×C33 | C2×C3⋊D3 |
| hypocenter | C32×H(3,𝔽3) | D4 |
| LCS | G ▷ C2×C32×H(3,𝔽3) ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C3⋊#272 | C2 | semidirect |
| 2. H(3,𝔽3)×C3⋊Dic3 | C2 | semidirect |
| 8. C32×C3⋊Dic3 | D3 | semidirect |
| 9. C2×C3⋊#272 | D3 | semidirect |
| 14. C32×H(3,𝔽3) | D4 | semidirect |
| 41. C34 | D12 | semidirect |
| 45. C3×H(3,𝔽3) | #67 | semidirect |
| 82. C3⋊Dic3 | #272 | semidirect |
| 93. C33 | #626 | semidirect |
| 98. H(3,𝔽3) | #625 | semidirect |
| 152. C32 | C4⋊#272 | semidirect |
| 154. C32 | #6295 | semidirect |
| 178. C3 | #10619893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊#272 | 2 |
| H(3,𝔽3)×C3⋊Dic3 | 2 |
| C3×#6295 | 3 |
| #10619893 | 3 |