Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
393 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#66362 | C2 |
| Frattini | C32 | C3⋊(C3⋊S4) |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | #272 |
| LCS | G ▷ C3×#66362 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#66362 | C2 | semidirect |
| 7. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 9. C3×C22⋊H(3,𝔽3) | D3 | semidirect |
| 10. C32×C22⋊C9 | D3 | semidirect |
| 12. #66362 | D3 | semidirect |
| 34. C22×H(3,𝔽3) | C3⋊D3 | semidirect |
| 37. C22⋊H(3,𝔽3) | C3⋊D3 | semidirect |
| 40. C3×C22⋊C9 | C3⋊D3 | semidirect |
| 43. C3×H(3,𝔽3) | S4 | semidirect |
| 91. H(3,𝔽3) | C3⋊S4 | semidirect |
| 120. C22×C3 | #4185 | semidirect |
| 152. C22 | C3⋊#4185 | semidirect |
| 158. C3 | #10619755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66362 | 2 |
| C3⋊((C3⋊S4)⋊C3) | 3 |
| C3×C3⋊((C22⋊C9)⋊C2) | 3 |
| #10619977 | 3 |
| #10619755 | 3 |
| C3⋊#4185 | 4 |