Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
487 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 487 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(C3⋊((C22⋊C9)⋊C2)) |
| commutator, cosocle, hypocenter | H(3,𝔽3)×C22⋊C9 | C2 |
| Frattini | C32 | C3⋊(C3⋊S4) |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | C3⋊(C3⋊D3) |
| LCS | G ▷ H(3,𝔽3)×C22⋊C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. H(3,𝔽3)×C22⋊C9 | C2 | semidirect |
| 8. C32×C22⋊C9 | D3 | semidirect |
| 10. C32⋊(C22⋊C9) | D3 | semidirect |
| 24. C22×H(3,𝔽3) | D9 | semidirect |
| 48. C22×C32 | C3⋊D9 | semidirect |
| 58. C22⋊C9 | #272 | semidirect |
| 60. H(3,𝔽3) | (C22⋊C9)⋊C2 | semidirect |
| 89. C32 | C3⋊((C22⋊C9)⋊C2) | semidirect |
| 103. C22 | C9⋊#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×C22⋊C9 | 2 |
| C3×C3⋊((C22⋊C9)⋊C2) | 3 |
| #10619994 | 3 |
| #10619761 | 3 |
| C9⋊#272 | 4 |