Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
234 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 32 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 | #10619744 |
| commutator, cosocle, hypocenter | C3×C22⋊C9 | C2×C32 |
| Frattini | C32 | C32×S4 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C3×C22⋊C9 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#66361 | C2 | semidirect |
| 2. C3×C3⋊((C22⋊C9)⋊C2) | C3 | semidirect |
| 4. #10619744 | C3 | direct (N × H) |
| 9. C32×C22⋊C9 | C2×C3 | semidirect |
| 12. #66361 | C2×C3 | semidirect |
| 16. C3⋊((C22⋊C9)⋊C2) | C32 | semidirect |
| 38. C3×C22⋊C9 | C2×C32 | semidirect |
| 120. C22×C3 | #4177 | semidirect |
| 152. C22 | C3×#4177 | semidirect |
| 158. C3 | #10619744 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#66361 | 2 |
| C3×C3⋊((C22⋊C9)⋊C2) | 3 |
| C3×#638⋊C3 | 3 |
| #10619744 | 3 |
| C3×#4177 | 4 |